A372124 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1 + 9*x)^(1/3) * A(x) ).

1, 1, 5, 8, 86, 12, 2418, -6015, 97271, -490693, 4991069, -33481184, 294850612, -2232642956, 18815166552, -150373925928, 1255171140378, -10300278908424, 86135158514634, -717384480699522, 6029697856319760, -50699911500290454, 428507430151063548

Offset: 0

Author

Seiichi Manyama, Apr 20 2024

Keywords

• sign

Crossrefs

Cf. A000108, A372137.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x*(1+9*x)^(1/3))))

PARI

a(n) = sum(k=0, n, 9^(n-k)*binomial(2*k, k)*binomial(k/3, n-k)/(k+1));

Formula

G.f.: A(x) = 2/(1 + sqrt(1-4*x*(1+9*x)^(1/3))).

a(n) = Sum_{k=0..n} 9^(n-k) * binomial(2*k,k) * binomial(k/3,n-k)/(k+1).