A378043 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^2 ).
1, 2, 13, 190, 4045, 116746, 4251289, 187255174, 9684799961, 575477786674, 38638577549701, 2893159369162030, 239045577899472997, 21604942464613062010, 2120362938300115706513, 224568728344893756230326, 25529660577970226603535793, 3100816199696659908092912866
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
-
PARI
a(n) = n!*sum(k=0, n, (2*k+1)^(k-1)*binomial(3*k+1, n-k)/k!);
Formula
E.g.f.: (1+x) * exp( -LambertW(-2*x*(1+x)^3)/2 ).
a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(3*k+1,n-k)/k!.