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
Keywords
Programs
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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;
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