A371392 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+2*x)^3 ).

1, 7, 68, 769, 9492, 124014, 1686120, 23610565, 338200148, 4932348226, 72993007672, 1093371638954, 16545598769416, 252567107648604, 3884497559034192, 60136704175071789, 936373570430169300, 14654788984834217850, 230405413840884827160, 3637362857723455772670

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

Prog

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

Crossrefs

Cf. A047891, A371391.

Cf. A113207.

Sequence in context: A297502 A087567 A328046 * A306386 A136629 A197525

Adjacent sequences: A371389 A371390 A371391 * A371393 A371394 A371395

Keyword

nonn

Author

Seiichi Manyama, Mar 21 2024

Status

approved