OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..451
FORMULA
a(0) = 1; a(n) = (n-1)!/6 * Sum_{k=4..n} k/(k-3) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/4)} |Stirling1(n-3*k,k)|/(6^k * (n-3*k)!).
a(n) ~ sqrt(2*Pi) * n^(n - 1/3) / (Gamma(1/6) * exp(n)). - Vaclav Kotesovec, May 04 2022
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)^(-x^3/6)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^3/6*log(1-x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/6*sum(j=4, i, j/(j-3)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\4, abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 02 2022
STATUS
approved