A366357 G.f. satisfies A(x) = 1/(1 - x) + x/A(x)^2.

1, 2, -3, 19, -105, 690, -4781, 34708, -260189, 1999169, -15660175, 124596499, -1004110947, 8179379808, -67239070867, 557098881920, -4647368670949, 39001655222788, -329048378867467, 2789241880512899, -23743798316713367, 202894843070927860

Offset: 0

Author

Seiichi Manyama, Oct 08 2023

Keywords

• sign

Crossrefs

Cf. A007317, A199475, A349289, A349290, A349291, A349292, A349293, A366356, A366358, A366359.

Cf. A364393, A366326, A366364.

Programs

PARI

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

Formula

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