A381879 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / C(x) ), where C(x) is the g.f. of A000108.

1, 3, 16, 106, 788, 6292, 52743, 457946, 4083328, 37174786, 344142192, 3229827900, 30661272627, 293907951057, 2840826401664, 27657352868946, 270968414904700, 2669604470832568, 26431802684789970, 262864480970961882, 2624640191306617088, 26301183967687772360

Offset: 0

Author

Seiichi Manyama, Mar 09 2025

Keywords

• nonn

Crossrefs

Cf. A381817, A381880.

Cf. A000108, A381881.

Programs

PARI

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

Formula

G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x*A(x))^2.

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