A381880 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / C(x) ), where C(x) is the g.f. of A000108.

1, 4, 27, 223, 2052, 20199, 208205, 2219149, 24261279, 270581313, 3066581130, 35216499786, 408919039968, 4792955710138, 56633333886618, 673881539636365, 8067939162382594, 97117925556632184, 1174721577627568371, 14270877151754826473, 174044527062280321368

Offset: 0

Author

Seiichi Manyama, Mar 09 2025

Keywords

• nonn

Crossrefs

Cf. A381817, A381879.

Cf. A000108, A381882.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3*2*x/(1-sqrt(1-4*x)))/x)

Formula

G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x*A(x))^3.

a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(4*n-k+2,n-k)/(n+2*k+1).