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A357598 Expansion of e.g.f. sinh(2 * (exp(x)-1)) / 2. 8
0, 1, 1, 5, 25, 117, 601, 3509, 22457, 153141, 1105561, 8453557, 68339833, 581495605, 5184047961, 48259748533, 468040609593, 4719817792565, 49396003390489, 535526127566773, 6004124908829177, 69509047405180213, 829801009239621849, 10202835010223731893 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Bell Polynomial.
FORMULA
a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * Stirling2(n,2*k+1).
a(n) = ( Bell_n(2) - Bell_n(-2) )/4, where Bell_n(x) is n-th Bell polynomial.
a(n) = 0; a(n) = Sum_{k=0..n-1} binomial(n-1, k) * A065143(k).
PROG
(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh(2*(exp(x)-1))/2)))
(PARI) a(n) = sum(k=0, (n-1)\2, 4^k*stirling(n, 2*k+1, 2));
(PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
a(n) = round((Bell_poly(n, 2)-Bell_poly(n, -2)))/4;
CROSSREFS
Sequence in context: A200781 A055297 A244828 * A238808 A034274 A110212
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 05 2022
STATUS
approved

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Last modified April 20 10:14 EDT 2024. Contains 371813 sequences. (Running on oeis4.)