A371404 Expansion of (1/x) * Series_Reversion( x / ( (1+x) * (1+3*x)^2 ) ).

1, 7, 64, 667, 7513, 89092, 1095832, 13852195, 178855075, 2348744095, 31273438804, 421224534100, 5728966150924, 78569975545432, 1085350298162608, 15087689038165555, 210907141968410071, 2962825568825439349, 41806163408065511032, 592244891188614804643

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} 3^k * binomial(2*(n+1),k) * binomial(n+1,n-k).

Prog

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

Crossrefs

Cf. A001764, A034015.

Sequence in context: A301424 A288690 A362726 * A213515 A349333 A293470

Adjacent sequences: A371401 A371402 A371403 * A371405 A371406 A371407

Keyword

nonn

Author

Seiichi Manyama, Mar 21 2024

Status

approved