A355507 Expansion of e.g.f. (1 - x)^(-x^4/24).

1, 0, 0, 0, 0, 5, 15, 70, 420, 3024, 28350, 272250, 2875950, 33333300, 420840420, 5763671550, 84799915200, 1334007397800, 22343877115560, 396971840865600, 7456250728017000, 147612122975772000, 3071792315894841000, 67030983483724953000, 1530448652869851191400

Offset

0,6

Links

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

Formula

a(0) = 1; a(n) = (n-1)!/24 * Sum_{k=5..n} k/(k-4) * a(n-k)/(n-k)!.

a(n) = n! * Sum_{k=0..floor(n/5)} |Stirling1(n-4*k,k)|/(24^k * (n-4*k)!).

a(n) ~ n! / (Gamma(1/24) * n^(23/24)). - Vaclav Kotesovec, Jul 21 2022

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)^(-x^4/24)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^4/24*log(1-x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/24*sum(j=5, i, j/(j-4)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\5, abs(stirling(n-4*k, k, 1))/(24^k*(n-4*k)!));

Crossrefs

Column k=4 of A355610.

Cf. A351493.

Sequence in context: A149640 A353173 A355603 * A259205 A149641 A149642

Adjacent sequences: A355504 A355505 A355506 * A355508 A355509 A355510

Keyword

nonn

Author

Seiichi Manyama, Jul 09 2022

Status

approved