A382089 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^4) ), where B(x) = 1 + x*B(x)^5 is the g.f. of A002294.
1, 1, 11, 268, 10301, 543576, 36542527, 2987431168, 287751180537, 31916479461760, 4006558784401811, 561568192339405824, 86932015931716588789, 14730649112418719484928, 2711977587454133506904775, 539042371050858695696121856, 115046065096051639979478349553
Offset: 0
Keywords
Programs
-
PARI
a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(4*n+k-1, 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-1,k)/(n-k-1)! for n > 0.
E.g.f.: exp( Series_Reversion( x * (1-x)^4 * exp(-x) ) ).