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

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..969

Robert Israel, Linear recurrence of order 8

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).

D-finite with linear recurrence of order 8 (see link). - Robert Israel, May 01 2026

Prog

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

Crossrefs

Cf. A381817, A381880.

Cf. A000108, A381881.

Sequence in context: A063548 A157452 A369694 * A074551 A135074 A292752

Adjacent sequences: A381876 A381877 A381878 * A381880 A381881 A381882

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2025

Status

approved