A380040 E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)) )^(2/3).

1, 2, 14, 170, 3000, 69930, 2033212, 70972734, 2894590064, 135164076722, 7113787010100, 416759006663142, 26903080612468744, 1897553477118350922, 145204649027247413996, 11982094054396851014030, 1060673494236770414806752, 100265097180082772515691874, 10080871201186661027182272868

Offset: 0

Author

Seiichi Manyama, Jan 10 2025

Keywords

• nonn

Crossrefs

Cf. A380039, A380041.

Programs

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380041.

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