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

0,3

Links

Table of n, a(n) for n=0..18.

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)! ).

Prog

(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)!));

Crossrefs

Cf. A380017, A380039.

Sequence in context: A354320 A230342 A239301 * A121958 A177555 A054746

Adjacent sequences: A380035 A380039 A380040 * A380042 A380043 A380044

Keyword

nonn,new

Author

Seiichi Manyama, Jan 10 2025

Status

approved