OFFSET
0,4
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 01 2022
STATUS
approved