A376382 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x) - 1))^3 ).
1, 0, 6, 9, 588, 3435, 196038, 2504271, 143382648, 3105223155, 186676465890, 5932031027703, 382522369695876, 16267245179116971, 1137287705462533758, 60811389044325205695, 4631220227358066139248, 298002734705467572715491, 24748409310987998502582138
Offset: 0
Keywords
Programs
-
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x)-1))^3)/x)) -
PARI
a(n) = 3*n!*sum(k=0, n\2, (3*n+k+2)!*stirling(n-k, k, 2)/(n-k)!)/(3*n+3)!;
Formula
E.g.f. A(x) satisfies A(x) = 1/(1 - x*A(x) * (exp(x*A(x)) - 1))^3.
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A371273.
a(n) = (3 * n!/(3*n+3)!) * Sum_{k=0..floor(n/2)} (3*n+k+2)! * Stirling2(n-k,k)/(n-k)!.