OFFSET
0,5
LINKS
Winston de Greef, Table of n, a(n) for n = 0..529
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)} Stirling2(n-3*k,k)/(6^k * (n-3*k)!).
MATHEMATICA
With[{nn=30}, CoefficientList[Series[Exp[x^3/6 (Exp[x]-1)], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 07 2023 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3/6*(exp(x)-1))))
(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, stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 13 2022
STATUS
approved