Question

Let hn (n ≥ 0) denote the number of n-digit integers such that each digit is odd and each of the digits 1, 3, 5, 7, 9 occurs an odd number of times.

score 308 · Answer 1 · 2020-05-04 18:23:28

Let hn (n ≥ 0) denote the number of n-digit integers such that each digit is odd and each of the digits 1, 3, 5, 7, 9 occurs an odd number of times.

score 103 · Answer 2 · 2020-05-04 23:18:27

103

Views

Understanding extended binomial theorem for coefficient in square roots

Published on 04 May 2020 - 23:18

score 144 · Answer 3 · 2026-03-30 11:17:12

144

Views

How to prove the closed form for the generating function $g_r(x) = \sum_{n=0}^\infty {n \choose r} x^n$ possibly using Newton's Binomial Theorem

Published on 30 Mar 2026 - 11:17

score 40 · Answer 4 · 2020-05-05 20:31:50

40

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What is the relation between the generating function and the extinction probability?

Published on 05 May 2020 - 20:31

score 107 · Answer 5 · 2026-03-27 23:57:34

107

Views

Why do we use exponents in characteristic function

Published on 27 Mar 2026 - 23:57

score 95 · Answer 6 · 2026-03-26 17:53:47

95

Views

Sum $\frac{1}{2}\sum_{\substack{n = 1 \\n \text{ odd}}}^{\infty} \sum_{k=0}^n \frac{x^k}{k!} \frac{x^{n-k}}{(n-k)!}$

Published on 26 Mar 2026 - 17:53

score 101 · Answer 7 · 2020-05-10 06:54:29

101

Views

Find a simple form for the EGF (in terms of $f(x)$)

Published on 10 May 2020 - 6:54

score 41 · Answer 8 · 2026-03-31 07:13:18

41

Views

How can I find a closed form of the ordinary generating function for sequences

Published on 31 Mar 2026 - 7:13

score 92 · Answer 9 · 2026-03-30 08:01:25

92

Views

Factorial derivatives and generating functions of natural powers

Published on 30 Mar 2026 - 8:01

score 31 · Answer 10 · 2020-05-11 11:44:05

31

Views

two generating functions and their limits

Published on 11 May 2020 - 11:44

score 61 · Answer 11 · 2020-05-12 11:15:25

61

Views

Generating functions formula

Published on 12 May 2020 - 11:15

score 353 · Answer 12 · 2020-05-12 13:36:41

353

Views

Tiling a $2 \times n$ rectangle by $2 \times 1$ rectangles and L-shapes : adapted generating functions

Published on 12 May 2020 - 13:36

score 157 · Answer 13 · 2020-05-12 15:47:51

157

Views

Fixed point of a generating function

Published on 12 May 2020 - 15:47

score 185 · Answer 14 · 2026-03-25 14:03:26

185

Views

Relationship between Poisson's integral formula and the generating function of Chebyshev polynomials

Published on 25 Mar 2026 - 14:03

score 387 · Answer 15 · 2026-03-25 07:41:03

387

Views

Generating function of Young Diagram from a given semiperimeter

Published on 25 Mar 2026 - 7:41

List Question

Let hn (n ≥ 0) denote the number of n-digit integers such that each digit is odd and each of the digits 1, 3, 5, 7, 9 occurs an odd number of times.

Understanding extended binomial theorem for coefficient in square roots

How to prove the closed form for the generating function $g_r(x) = \sum_{n=0}^\infty {n \choose r} x^n$ possibly using Newton's Binomial Theorem

What is the relation between the generating function and the extinction probability?

Why do we use exponents in characteristic function

Sum $\frac{1}{2}\sum_{\substack{n = 1 \\n \text{ odd}}}^{\infty} \sum_{k=0}^n \frac{x^k}{k!} \frac{x^{n-k}}{(n-k)!}$

Find a simple form for the EGF (in terms of $f(x)$)

How can I find a closed form of the ordinary generating function for sequences

Factorial derivatives and generating functions of natural powers

two generating functions and their limits

Generating functions formula

Tiling a $2 \times n$ rectangle by $2 \times 1$ rectangles and L-shapes : adapted generating functions

Fixed point of a generating function

Relationship between Poisson's integral formula and the generating function of Chebyshev polynomials

Generating function of Young Diagram from a given semiperimeter

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