A357968 Expansion of e.g.f. exp( x * (exp(x^4) - 1) ).

1, 0, 0, 0, 0, 120, 0, 0, 0, 181440, 1814400, 0, 0, 1037836800, 43589145600, 217945728000, 0, 14820309504000, 1867358997504000, 30411275102208000, 101370917007360000, 425757851430912000, 140500090972200960000, 5385836820601036800000

Offset

0,6

Links

Harvey P. Dale, Table of n, a(n) for n = 0..467

Formula

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

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x (Exp[x^4]-1)], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 29 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^4)-1))))
(PARI) a(n) = n!*sum(k=0, n\4, stirling(k, n-4*k, 2)/k!);

Crossrefs

Cf. A357966, A357967.

Sequence in context: A196429 A243779 A267335 * A392796 A392793 A156415

Adjacent sequences: A357965 A357966 A357967 * A357969 A357970 A357971

Keyword

nonn

Author

Seiichi Manyama, Oct 22 2022

Status

approved