A377860 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(x) ).
1, 1, 5, 44, 577, 10104, 222133, 5886880, 182775969, 6509571200, 261665344261, 11720054882304, 578878362625825, 31259890045425664, 1832295378792935925, 115862322601669627904, 7861907382202262095297, 569837358810005613281280, 43939338917141224534941829
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (-1)^k*(n+1)^(k-1)*binomial(3*n-k+1, n-k)/k!);
Formula
E.g.f. A(x) satisfies A(x) = exp(-x * A(x))/(1 - x*A(x))^2.
a(n) = n! * Sum_{k=0..n} (-1)^k * (n+1)^(k-1) * binomial(3*n-k+1,n-k)/k!.