A385474 Expansion of (1/x) * Series_Reversion( x * (1-2*x)^2 / (1+x)^3 ).

1, 7, 76, 991, 14281, 219172, 3512440, 58096591, 984340003, 16996883887, 298017184048, 5291703108292, 94961611382860, 1719543577996888, 31379622840361696, 576519956457976495, 10655055147825932119, 197959348525977645781, 3695112941037246866044

Offset: 0

Author

Seiichi Manyama, Aug 01 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A064063, A385475.

Cf. A384950.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^2/(1+x)^3)/x)

PARI

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

Formula

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

a(n) = (1/(n+1)) * [x^n] ( (1+x)^3 / (1-2*x)^2 )^(n+1).