A371367 Expansion of (1/x) * Series_Reversion( x * (1-6*x)^2 / (1-5*x) ).

1, 7, 97, 1675, 32353, 669103, 14491441, 324479203, 7450571905, 174479758615, 4151241723265, 100060420474555, 2438221991122657, 59964761207220415, 1486507438771416529, 37105090783548992659, 931807879987468872193, 23525616974931980536615

Offset: 0

Author

Seiichi Manyama, Mar 19 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A078018.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-6*x)^2/(1-5*x))/x)

PARI

a(n) = sum(k=0, n, 5^(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} 5^(n-k) * binomial(2*n+k+1,k) * binomial(2*n,n-k).