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A357572 Expansion of e.g.f. sinh(sqrt(3) * (exp(x)-1)) / sqrt(3). 7
0, 1, 1, 4, 19, 85, 406, 2191, 13105, 84190, 573121, 4127521, 31434184, 252388957, 2126998693, 18740283556, 172134162631, 1644920020417, 16324076578870, 167938152551491, 1787952325142341, 19667748794844550, 223217829954224029, 2610546296216999197 (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)} 3^k * Stirling2(n,2*k+1).
a(n) = ( Bell_n(sqrt(3)) - Bell_n(-sqrt(3)) )/(2 * sqrt(3)), where Bell_n(x) is n-th Bell polynomial.
a(n) = 0; a(n) = Sum_{k=0..n-1} binomial(n-1, k) * A357615(k).
PROG
(PARI) a(n) = sum(k=0, (n-1)\2, 3^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, sqrt(3))-Bell_poly(n, -sqrt(3)))/(2*sqrt(3)));
CROSSREFS
Sequence in context: A017962 A260746 A290667 * A291416 A192526 A084155
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 05 2022
STATUS
approved

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Last modified May 18 15:24 EDT 2024. Contains 372664 sequences. (Running on oeis4.)