A378093 E.g.f. satisfies A(x) = exp( x * (1-x)^2 * A(x)^3 ) / (1-x).
1, 2, 13, 187, 4421, 145381, 6106885, 312010217, 18775791529, 1300609323577, 101932831136801, 8917429459192717, 861423205666601869, 91071085791088039781, 10459294205668851438589, 1296711971347861868098561, 172604468588739615868724945, 24551969347625035312300681969
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
-
PARI
a(n) = n!*sum(k=0, n, (3*k+1)^(k-1)*binomial(n, k)/k!);
Formula
E.g.f.: exp( -LambertW(-3*x/(1-x))/3 )/(1-x).
a(n) = n! * Sum_{k=0..n} (3*k+1)^(k-1) * binomial(n,k)/k!.