OFFSET
0,4
FORMULA
E.g.f. A(x) satisfies A(x) = 1/(1 - x*A(x) * (exp(x^2*A(x)^2) - 1))^3.
a(n) = (3 * n!/(3n+3)!) * Sum_{k=0..floor(n/2)} (4*n-2*k+2)! * Stirling2(k,n-2*k)/k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1))^3)/x))
(PARI) a(n) = 3*n!*sum(k=0, n\2, (4*n-2*k+2)!*stirling(k, n-2*k, 2)/k!)/(3*n+3)!;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 22 2024
STATUS
approved