A353224 Expansion of e.g.f. (1 - x^4)^(-1/x).

1, 0, 0, 6, 0, 0, 360, 2520, 0, 60480, 1814400, 13305600, 19958400, 1556755200, 39956716800, 337815878400, 1743565824000, 103742166528000, 2676547896422400, 26863293006950400, 287217598187520000, 15976056520359936000, 432428057769996288000

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (4*exp(n)). - Vaclav Kotesovec, May 04 2022

Prog

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

Crossrefs

Cf. A121452, A353222.

Cf. A353225.

Sequence in context: A230787 A360424 A101109 * A293526 A293568 A192072

Adjacent sequences: A353221 A353222 A353223 * A353225 A353226 A353227

Keyword

nonn

Author

Seiichi Manyama, May 01 2022

Status

approved