A380800 Expansion of e.g.f. ( (1/x) * Series_Reversion( x * exp(-x / (1 - x)^2) * (1 - x)^3 ) )^2.
1, 8, 142, 4088, 165576, 8711752, 566093104, 43882188408, 3957135262720, 407285038758536, 47138933615042304, 6062383519783848952, 857919091977394542592, 132511278843714141837000, 22185703881021997753194496, 4002648943012304165391154808, 774212130931445685605345918976
Offset: 0
Keywords
Programs
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PARI
a(n, q=2, r=1, s=1, t=2, u=3) = 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( 2 * x * A(x)^(1/2) / (1 - x*A(x)^(1/2))^2 ) / (1 - x*A(x)^(1/2))^6.
a(n) = 2 * n! * Sum_{k=0..n} (n+2)^(k-1) * binomial(4*n+k+5,n-k)/k!.