A371406 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+2*x)^2 ) ).

1, 6, 49, 462, 4734, 51216, 575705, 6657846, 78703438, 946740132, 11551512042, 142616584380, 1778372098000, 22365031140900, 283341912929865, 3612782260978470, 46326552943960278, 597034029166804068, 7728885814331709374, 100458438481544424996

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for reversions of series

Formula

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

a(n) = A219538(n+1)/2. - Seiichi Manyama, Dec 24 2024

a(n) = (1/(n+1)) * [x^n] ( (1+x) * (1+2*x) )^(2*(n+1)). - Seiichi Manyama, Dec 25 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+2*x)^2))/x)
(PARI) a(n) = sum(k=0, n, 2^k*binomial(2*(n+1), k)*binomial(2*(n+1), n-k))/(n+1);

Crossrefs

Cf. A219538, A371398.

Cf. A379546, A379547.

Sequence in context: A104170 A098306 A055847 * A365193 A365188 A143165

Adjacent sequences: A371403 A371404 A371405 * A371407 A371408 A371409

Keyword

nonn

Author

Seiichi Manyama, Mar 21 2024

Status

approved