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Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?

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#combinatorics #summation #generating-functions #closed-form #stirling-numbers
280
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Stirling number of second kind S(m,4)

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#combinatorics #discrete-mathematics #stirling-numbers #set-partition
309
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Any good approximations for Stirling numbers?

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#combinatorics #combinations #stirling-numbers
507
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Recurrence relation, unsigned stirling numbers of first kind

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#combinatorics #recurrence-relations #stirling-numbers
151
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Surjections using Stirling-numbers

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#combinatorics #discrete-mathematics #stirling-numbers
1.7k
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Proof of Dobinski's formula for Bell numbers

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#combinatorics #stirling-numbers
921
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prove $\sum_{k=0}^n(-1)^k k!S_k^n = (-1)^n $

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#combinatorics #discrete-mathematics #combinations #stirling-numbers
85
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Expression of the n-th derivative

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#combinatorics #derivatives #stirling-numbers
432
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Combinatorial interpretation of q-analog Stirling numbers of the second kind

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#combinatorics #stirling-numbers #q-analogs
396
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Evaluate sum involving stirling numbers of second kind using EGF

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#combinatorics #generating-functions #stirling-numbers
159
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Bell partial numbers

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#combinatorics #reference-request #stirling-numbers #set-partition
81
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Exact Expression for the n-th Derivative

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#combinatorics #derivatives #stirling-numbers
140
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Striling number of second kind when each partition has at least $r $ elements

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#combinatorics #recurrence-relations #stirling-numbers
126
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Solution of this recurrence relation

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#combinatorics #graph-theory #recurrence-relations #trees #stirling-numbers
1.1k
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Stirling Numbers: Proof $S(n+1,m) = \sum_{k=0}^{n} {n \choose k}S(k,m-1)$

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