OFFSET
0,4
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} k^(n-2*k) * binomial(n-2*k+1,k)/( 2^k*(n-2*k+1)*(n-2*k)! ).
MATHEMATICA
nmax = 20; CoefficientList[Series[1 - LambertW[-E^x*x^3/2]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 10 2024 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)*binomial(n-2*k+1, k)/(2^k*(n-2*k+1)*(n-2*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 09 2024
STATUS
approved