A379521 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^3 * (1+2*x)^2 ) ).

1, 7, 68, 767, 9425, 122436, 1653776, 22992655, 326863667, 4729547023, 69424933968, 1031309398852, 15474833826028, 234201961398776, 3570887895432504, 54799089019823407, 845757173849239415, 13119400228929684885, 204429551432900950068, 3198423097762769254279, 50225078058311068601425

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for reversions of series

Formula

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

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3*(1+2*x)^2))/x)
(PARI) a(n) = sum(k=0, n, 2^k*binomial(2*(n+1), k)*binomial(3*(n+1), n-k))/(n+1);

Crossrefs

Cf. A243659, A379522.

Sequence in context: A297502 A087567 A328046 * A371392 A306386 A136629

Adjacent sequences: A379518 A379519 A379520 * A379522 A379524 A379525

Keyword

nonn

Author

Seiichi Manyama, Dec 24 2024

Status

approved