A386722 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1+2*x)^3 ).

1, 8, 91, 1214, 17731, 274526, 4426948, 73561238, 1250803171, 21659155028, 380638861219, 6771681469952, 121716110229364, 2207040281944856, 40323735229993336, 741613603443652214, 13718779315483616227, 255086483631977702096, 4764893748897482791633, 89373590789286772582334

Offset: 0

Author

Seiichi Manyama, Jul 31 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A371391, A386723.

Cf. A385320.

Programs

PARI

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

PARI

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

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