A371431 Expansion of (1/x) * Series_Reversion( x * ((1-x)^2 + x^3) ).

1, 2, 7, 29, 131, 623, 3064, 15423, 78936, 408958, 2137993, 11252163, 59508232, 315786764, 1679410076, 8941421014, 47613443433, 253359512287, 1346009853489, 7133000408765, 37669665812955, 198034693198875, 1035095172883710, 5371011415598595, 27615259784888724

Offset: 0

Author

Seiichi Manyama, Mar 23 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369214.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\3, (-1)^k*binomial(n+k, k)*binomial(3*n-k+1, n-3*k))/(n+1);

Formula

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