A382038 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^4) ), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.
1, 1, 11, 244, 8285, 381096, 22175167, 1562582848, 129381990201, 12313784396800, 1324663415429651, 158957183013686784, 21051725357219126869, 3050121640032545419264, 479928476696367747954375, 81499293517054315684642816, 14856515462975583258374526833, 2893604521320117995839047401472
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(4*n, k)/(n-k-1)!));
Formula
E.g.f. A(x) satisfies A(x) = exp(x*A(x) * B(x*A(x))^4).
a(n) = (n-1)! * Sum_{k=0..n-1} (n+1)^(n-k-1) * binomial(4*n,k)/(n-k-1)! for n > 0.
E.g.f.: exp( Series_Reversion( x*exp(-x)/(1+x)^4 ) ).