A380826 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x) / (1 + x*exp(-2*x)) ).
1, 4, 43, 810, 22273, 811728, 36979467, 2025462736, 129748802401, 9522843081984, 788169731306059, 72641846664240384, 7379343546762675873, 819269203286474309632, 98698960328223628470379, 12824232015954542746048512, 1787731339345567827140060737, 266157254062414638948185210880
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (n+2*k+3)^k*binomial(n, k)/(k+1)!);
Formula
E.g.f. A(x) satisfies A(x) = exp(3*x*A(x)) / ( 1 - x*exp(x*A(x)) ).
a(n) = n! * Sum_{k=0..n} (n+2*k+3)^k * binomial(n,k)/(k+1)!.