OFFSET
0,5
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n-3*k+1,k)/( 6^k*(n-3*k+1)*(n-3*k)! ).
MATHEMATICA
nmax = 20; CoefficientList[Series[1 - ProductLog[-E^x*x^4/6]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 10 2024 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-3*k+1, k)/(6^k*(n-3*k+1)*(n-3*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 09 2024
STATUS
approved