OFFSET
0,4
FORMULA
E.g.f. A(x) satisfies A(x) = 1/(1 - x^2*A(x)^2 * (exp(x*A(x)) - 1))^3.
a(n) = (3 * n!/(3*n+3)!) * Sum_{k=0..floor(n/3)} (3*n+k+2)! * Stirling2(n-2*k,k)/(n-2*k)!.
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2*(exp(x)-1))^3)/x))
(PARI) a(n) = 3*n!*sum(k=0, n\3, (3*n+k+2)!*stirling(n-2*k, k, 2)/(n-2*k)!)/(3*n+3)!;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 22 2024
STATUS
approved