A380946 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^3 * exp(-3*x) ).
1, 6, 111, 3678, 179073, 11588688, 938905551, 91542271824, 10444685410881, 1365936450693120, 201503447217869679, 33108736185915906816, 5997057218957213126721, 1187319940110958086623232, 255104922613608981003351375, 59120580081196768991316314112
Offset: 0
Keywords
Programs
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PARI
a(n, q=3, r=3, s=3, t=0, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);
Formula
E.g.f. A(x) satisfies A(x) = exp(3*x*A(x))/(1 - x*A(x))^3.
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A380724.
a(n) = 3 * n! * Sum_{k=0..n} (3*n+3)^(k-1) * binomial(4*n-k+2,n-k)/k!.