A357572 Expansion of e.g.f. sinh(sqrt(3) * (exp(x)-1)) / sqrt(3).

0, 1, 1, 4, 19, 85, 406, 2191, 13105, 84190, 573121, 4127521, 31434184, 252388957, 2126998693, 18740283556, 172134162631, 1644920020417, 16324076578870, 167938152551491, 1787952325142341, 19667748794844550, 223217829954224029, 2610546296216999197

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..562

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

Cf. A024429, A264037, A357598.

Cf. A027710, A357615, A357737.

Sequence in context: A017962 A260746 A290667 * A291416 A192526 A084155

Adjacent sequences: A357569 A357570 A357571 * A357573 A357574 A357575

Keyword

nonn

Author

Seiichi Manyama, Oct 05 2022

Status

approved