A354396 Expansion of e.g.f. exp( -(exp(x) - 1)^3 / 6 ).

1, 0, 0, -1, -6, -25, -80, -91, 1694, 23155, 206340, 1442969, 6928394, -6507865, -752409840, -12953182971, -160186016906, -1548849362085, -9789241693220, 28359195353489, 2378650585685794, 52832659521004495, 855581150441210600, 10878338100191146749

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n-1,k-1) * Stirling2(k,3) * a(n-k).

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling2(n,3*k)/((-6)^k * k!).

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[-(Exp[x]-1)^3/6], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 02 2023 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-(exp(x)-1)^3/6)))
(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, 3, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 2)/((-6)^k*k!));

Crossrefs

Cf. A000587, A354395, A354397, A354398.

Cf. A327504, A354392.

Sequence in context: A278473 A281157 A346975 * A256859 A133714 A164271

Adjacent sequences: A354393 A354394 A354395 * A354397 A354398 A354399

Keyword

sign

Author

Seiichi Manyama, May 25 2022

Status

approved