A380039 E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)) )^(1/3).

1, 1, 6, 61, 908, 17865, 438286, 12901735, 443475432, 17443879057, 773018191610, 38117147134671, 2070381313048588, 122841147634754185, 7905667340470592070, 548555101319868261655, 40825552788531622527056, 3244188226183716688784289, 274164589130871765969460594

Offset: 0

Author

Seiichi Manyama, Jan 10 2025

Keywords

• nonn

Crossrefs

Cf. A380017, A380041.

Cf. A380040.

Programs

PARI

a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(n/3+2*k/3+1/3, k)/((n+2*k+1)*(n-k)!));

Formula

a(n) = n! * Sum_{k=0..n} 3^k * k^(n-k) * binomial(n/3+2*k/3+1/3,k)/( (n+2*k+1)*(n-k)! ).