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%I #16 May 04 2022 05:05:47
%S 1,0,0,6,0,0,360,2520,0,60480,1814400,13305600,19958400,1556755200,
%T 39956716800,337815878400,1743565824000,103742166528000,
%U 2676547896422400,26863293006950400,287217598187520000,15976056520359936000,432428057769996288000
%N Expansion of e.g.f. (1 - x^4)^(-1/x).
%F 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)!.
%F a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (4*exp(n)). - _Vaclav Kotesovec_, May 04 2022
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^4)^(-1/x)))
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-log(1-x^4)/x)))
%o (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;
%Y Cf. A121452, A353222.
%Y Cf. A353225.
%K nonn
%O 0,4
%A _Seiichi Manyama_, May 01 2022
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