A354624 - OEIS

A354624

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

1, 0, 0, 0, 0, 120, 360, 1680, 10080, 72576, 2419200, 25660800, 279417600, 3286483200, 41894012160, 794511244800, 13755488947200, 238514695372800, 4269265386946560, 79696849513881600, 1658065431859200000

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(0) = 1; a(n) = (n-1)! * 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)|/(n-4*k)!.

a(n) ~ n! * (1 - 4/n - 16*log(n)/n^2). - Vaclav Kotesovec, Jul 21 2022

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)^(-x^4)))

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^4*log(1-x))))

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*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))/(n-4*k)!);

CROSSREFS

Column k=4 of A355609.

Cf. A353228, A353229.

Cf. A354625.

Sequence in context: A321841 A052778 A354625 * A226884 A273509 A147983

Adjacent sequences: A354621 A354622 A354623 * A354625 A354626 A354627

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jul 09 2022

STATUS

approved