A363818 G.f. satisfies A(x) = (1 + x/A(x)^2)/(1 - x)^2.

1, 3, -1, 24, -125, 924, -6895, 54181, -438737, 3639655, -30769033, 264122781, -2296010693, 20171456222, -178818115155, 1597550237324, -14369097515939, 130010781029079, -1182520161325459, 10806114831458755, -99163805247182631, 913441732959868748

Offset: 0

Author

Seiichi Manyama, Oct 18 2023

Keywords

• sign

Crossrefs

Cf. A162477, A363816, A364629, A364630.

Cf. A363819, A366364.

Programs

PARI

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

Formula

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