A381939 G.f. A(x) satisfies A(x) = (1 + x)^3 * B(x*A(x)), where B(x) is the g.f. of A001764.

1, 4, 13, 74, 568, 4872, 44576, 425936, 4199616, 42404096, 436238592, 4556085248, 48179319808, 514825553408, 5550284218368, 60296483084288, 659417378381824, 7253858445852672, 80209754567786496, 891027699137609728, 9939286070426992640, 111286739309529858048

Offset: 0

Author

Seiichi Manyama, Mar 10 2025

Keywords

• nonn

Crossrefs

Cf. A366695, A381860, A381942.

Cf. A001764, A367641.

Programs

PARI

a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(3*k+3, n-k)/(4*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(3*k+3,n-k)/(4*k+1).

a(n) = A367641(n) + A367641(n-1).