A354397 Expansion of e.g.f. exp( -(exp(x) - 1)^4 / 24 ).

1, 0, 0, 0, -1, -10, -65, -350, -1666, -6510, -7855, 270050, 4948669, 63503440, 702095030, 6924754200, 58870214129, 356043924590, -615569993285, -74306502570650, -1783956267419536, -32695418069393310, -520090808927130925, -7317310078355307250, -87056749651694635451

Offset

0,6

Links

Table of n, a(n) for n=0..24.

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n-1,k-1) * Stirling2(k,4) * a(n-k).

a(n) = Sum_{k=0..floor(n/4)} (4*k)! * Stirling2(n,4*k)/((-24)^k * k!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-(exp(x)-1)^4/24)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i-1, j-1)*stirling(j, 4, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\4, (4*k)!*stirling(n, 4*k, 2)/((-24)^k*k!));

Crossrefs

Cf. A000587, A354395, A354396, A354398.

Cf. A327505, A354393.

Sequence in context: A022638 A354393 A346976 * A003519 A056280 A000453

Adjacent sequences: A354394 A354395 A354396 * A354398 A354399 A354400

Keyword

sign

Author

Seiichi Manyama, May 25 2022

Status

approved