A371369 Expansion of (1/x) * Series_Reversion( x * (1-8*x)^2 / (1-7*x) ).

1, 9, 161, 3593, 89729, 2399817, 67222433, 1946874569, 57824172545, 1751650872713, 53910484818849, 1680961253003401, 52987626458710657, 1685806021244435913, 54062032254640697505, 1745723303156237416265, 56713604222408801019905

Offset: 0

Author

Seiichi Manyama, Mar 19 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A082147.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-8*x)^2/(1-7*x))/x)

PARI

a(n) = sum(k=0, n, 7^(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} 7^(n-k) * binomial(2*n+k+1,k) * binomial(2*n,n-k).