A380723 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2) / (1 - x*A(x)^2).

1, 2, 21, 436, 13785, 589206, 31825381, 2080523880, 159761186577, 14097898530730, 1405926737063541, 156379679761925148, 19195200442017128425, 2577494115099820986174, 375845854490491567916805, 59145488004443221188738256, 9990898494797767848442559649, 1803160967691789114062089511250

Offset: 0

Author

Seiichi Manyama, Jan 30 2025

Keywords

• nonn

Crossrefs

Cf. A377831, A380724.

Cf. A371318, A377888.

Cf. A360601, A380718.

Programs

PARI

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

Formula

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