A380829 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x) / (1 + x*exp(-x)) ).
1, 4, 45, 891, 25757, 986653, 47235873, 2718521725, 182963698521, 14107443728553, 1226582182222469, 118751669770995913, 12671598073554789909, 1477709279563430592877, 186988047586389278202633, 25518989446806209718773157, 3736444151435292273253963313, 584269287631534621583659461841
Offset: 0
Keywords
Programs
-
PARI
a(n) = n!*sum(k=0, n, (2*n+k+3)^k*binomial(n, k)/(k+1)!);
Formula
E.g.f. A(x) satisfies A(x) = exp(3*x*A(x)) / ( 1 - x*exp(2*x*A(x)) ).
a(n) = n! * Sum_{k=0..n} (2*n+k+3)^k * binomial(n,k)/(k+1)!.