A380041 E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)^2) )^(1/3).
1, 1, 6, 67, 1124, 25325, 718606, 24629395, 990296504, 45718478137, 2383877762810, 138578689119431, 8887132981365508, 623319005140469989, 47465740413056117894, 3900149351529967753435, 343951717449176947732976, 32405206661688405897284849, 3248370338004030319683766642
Offset: 0
Keywords
Programs
-
PARI
a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(2*n/3+k/3+1/3, k)/((2*n+k+1)*(n-k)!));
Formula
a(n) = n! * Sum_{k=0..n} 3^k * k^(n-k) * binomial(2*n/3+k/3+1/3,k)/( (2*n+k+1)*(n-k)! ).