A357666 Expansion of e.g.f. sinh( (exp(4*x) - 1)/2 )/2.

0, 1, 4, 20, 160, 1872, 25024, 348224, 5055488, 78571776, 1332573184, 24695206912, 493816963072, 10492449771520, 234399640633344, 5480635606908928, 134015043318054912, 3427700843478056960, 91642829715498336256, 2556218693498006929408

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} 4^(n-1-k) * Stirling2(n,2*k+1).

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh((exp(4*x)-1)/2)/2)))
(PARI) a(n) = sum(k=0, (n-1)\2, 4^(n-1-k)*stirling(n, 2*k+1, 2));

Crossrefs

Cf. A024429, A357664, A357665.

Cf. A357598, A357617, A357663.

Sequence in context: A094651 A065526 A032333 * A366639 A068965 A185672

Adjacent sequences: A357663 A357664 A357665 * A357667 A357668 A357669

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2022

Status

approved