A381912 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / B(x) ), where B(x) is the g.f. of A001764.

1, 3, 17, 124, 1038, 9470, 91586, 923542, 9608323, 102403921, 1112500651, 12275235274, 137193964646, 1549964417407, 17672282336488, 203092563108610, 2350061579393077, 27357919380212638, 320186582453226290, 3765185566095185740, 44465070300433434901, 527131055014319691537

Offset: 0

Author

Seiichi Manyama, Mar 10 2025

Keywords

• nonn

Crossrefs

Cf. A381911, A381913.

Cf. A381879, A381915.

Cf. A001764.

Programs

PARI

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

Formula

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

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