A371519 G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1-x))^5.

1, 5, 45, 470, 5375, 65231, 825225, 10764185, 143739440, 1955340360, 27001732972, 377530388235, 5333865386885, 76031188364860, 1092117166466660, 15792298241897649, 229704197116753825, 3358528175751886765, 49333470827844265285, 727680248026484478405

Offset: 0

Author

Seiichi Manyama, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A349333, A371379, A371521, A371522, A371523.

Cf. A270386, A371483, A371486.

Cf. A130564.

Programs

PARI

a(n) = sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+4, k)/(k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+4,k)/(k+1).

G.f.: A(x) = B(x/(1-x)), where B(x) = (1/x) * Series_Reversion( x*(1-x)^5 ).

G.f.: A(x) = B(x)^5 where B(x) is the g.f. of A349333.