Question

Simplifying a generating function in two variables with two binomial coefficients

score 388 · Answer 1 · 2026-03-30 16:00:32

388

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Simplifying a generating function in two variables with two binomial coefficients

Published on 30 Mar 2026 - 16:00

score 122 · Answer 2 · 2014-07-29 18:13:01

122

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Simplify this summation: $\sum\limits_{k=5}^\infty{\binom{k-1}{k-5}}\frac{k^3}{2^k}$

Published on 29 Jul 2014 - 18:13

score 192 · Answer 3 · 2014-07-30 01:27:09

192

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Simplifying $\displaystyle\sum_{k=0}^{20}(k+4)\binom{23-k}{3}$

Published on 30 Jul 2014 - 1:27

score 92 · Answer 4 · 2026-03-30 16:10:01

92

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Lower bound for a relative of the central binomial coeff

Published on 30 Mar 2026 - 16:10

score 327 · Answer 5 · 2014-07-30 09:58:02

327

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How to simplify a sum with binomial coefficients multiplied by $k^3/2^k$?

Published on 30 Jul 2014 - 9:58

score 324 · Answer 6 · 2014-07-31 15:54:29

324

Views

A double sum with combinatorial factors

Published on 31 Jul 2014 - 15:54

score 583 · Answer 7 · 2014-07-31 16:37:40

583

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The probability that after repeated random drawing from an urn, all balls left in the urn will be red

Published on 31 Jul 2014 - 16:37

score 128 · Answer 8 · 2014-08-01 14:54:21

128

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Multiple sum involving binomial factors

Published on 01 Aug 2014 - 14:54

score 271 · Answer 9 · 2014-08-02 09:18:42

271

Views

How to find the limit superior of the nth root of the generalized binomial coefficient?

Published on 02 Aug 2014 - 9:18

score 100 · Answer 10 · 2014-08-03 12:16:25

100

Views

A summation with binomial coefficients

Published on 03 Aug 2014 - 12:16

score 1.8k · Answer 11 · 2026-03-27 23:48:38

1.8k

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Behavior of Pascal's triangle in $n\mod m$ where $m>2$, any fractals?

Published on 27 Mar 2026 - 23:48

score 4.4k · Answer 12 · 2014-08-05 09:54:05

4.4k

Views

Truncated alternating binomial sum

Published on 05 Aug 2014 - 9:54

score 141 · Answer 13 · 2026-03-25 16:02:33

141

Views

Given the sequence $3, 4, 11, 16, 42\ldots $ how can I derive a general formula for it?

Published on 25 Mar 2026 - 16:02

score 260 · Answer 14 · 2026-04-01 03:27:53

260

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Conjecture for product of binomial coefficient

Published on 01 Apr 2026 - 3:27

score 50 · Answer 15 · 2026-03-30 16:09:55

50

Views

For each integer $s$, how many N-tuples with possible elements $\{0, 1, -1\}$ satisfy the condition that the sum of its elements is $s$?

Published on 30 Mar 2026 - 16:09

List Question

Simplifying a generating function in two variables with two binomial coefficients

Simplify this summation: $\sum\limits_{k=5}^\infty{\binom{k-1}{k-5}}\frac{k^3}{2^k}$

Simplifying $\displaystyle\sum_{k=0}^{20}(k+4)\binom{23-k}{3}$

Lower bound for a relative of the central binomial coeff

How to simplify a sum with binomial coefficients multiplied by $k^3/2^k$?

A double sum with combinatorial factors

The probability that after repeated random drawing from an urn, all balls left in the urn will be red

Multiple sum involving binomial factors

How to find the limit superior of the nth root of the generalized binomial coefficient?

A summation with binomial coefficients

Behavior of Pascal's triangle in $n\mod m$ where $m>2$, any fractals?

Truncated alternating binomial sum

Given the sequence $3, 4, 11, 16, 42\ldots $ how can I derive a general formula for it?

Conjecture for product of binomial coefficient

For each integer $s$, how many N-tuples with possible elements $\{0, 1, -1\}$ satisfy the condition that the sum of its elements is $s$?

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