A379862 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x)/(1 + x*exp(x))^2 ).
1, 3, 29, 502, 12761, 430986, 18217813, 926514058, 55133781809, 3760088111938, 289240874117981, 24780044801646762, 2340229465310736073, 241563626661550193794, 27059024800372108029221, 3269263894468329061597546, 423798837014001794141132897, 58674726188995774863597090690
Offset: 0
Keywords
Programs
-
PARI
a(n) = n!*sum(k=0, n, (n+k+1)^(n-k)*binomial(2*n+2, k)/(n-k)!)/(n+1);
Formula
E.g.f. A(x) satisfies A(x) = exp(x*A) * (1 + x * A(x) * exp(x*A(x)))^2.
a(n) = (n!/(n+1)) * Sum_{k=0..n} (n+k+1)^(n-k) * binomial(2*n+2,k)/(n-k)!.