A377833 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^3 * exp(-x) ).
1, 4, 51, 1174, 39833, 1799136, 101821723, 6938396368, 553482404721, 50619262481920, 5223014483031491, 600332651141435136, 76075005337204547209, 10538051760153093320704, 1584264031801742560408875, 256912816791069951740348416, 44703731640012047610981808097
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(4*n-k+2, n-k)/k!);
Formula
E.g.f. A(x) satisfies A(x) = exp(x * A(x))/(1 - x*A(x))^3.
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(4*n-k+2,n-k)/k!.