login
A376439
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2*(exp(x) - 1))^3 ).
0
1, 0, 0, 18, 36, 60, 23850, 189126, 988008, 184207176, 3254640750, 35132272890, 4418970811596, 134653558474188, 2463781708180338, 246532610826062190, 11098269938629561680, 305828547775319369616, 27016544700449293891158
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
Cf. A375663.
Sequence in context: A154575 A344199 A375663 * A097926 A087967 A070224
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 22 2024
STATUS
approved