A371368 Expansion of (1/x) * Series_Reversion( x * (1-7*x)^2 / (1-6*x) ).

1, 8, 127, 2514, 55679, 1320530, 32800020, 842314362, 22182639823, 595816941756, 16259068712391, 449504473152288, 12563255467347012, 354392729335581224, 10076681024065204760, 288500953324319325402, 8310071739586606559151

Offset: 0

Author

Seiichi Manyama, Mar 19 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A081178.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-7*x)^2/(1-6*x))/x)

PARI

a(n) = sum(k=0, n, 6^(n-k)*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} 6^(n-k) * binomial(2*n+k+1,k) * binomial(2*n,n-k).