A371436 Expansion of (1/x) * Series_Reversion( x * ((1-x)^4 + x) ).

1, 3, 12, 49, 179, 441, -860, -23634, -229246, -1705649, -10757370, -57800600, -246084657, -551185526, 3612960360, 66196180728, 641858169138, 4911870929096, 31792139997384, 172691510260794, 711428107177975, 1066704835555530, -18659356513414560

Offset: 0

Author

Seiichi Manyama, Mar 23 2024

Keywords

• sign

Links

• Index entries for reversions of series

Crossrefs

Cf. A369124, A369216.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^4+x))/x)

PARI

a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(5*n+3*k+3, n-k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(n+k,k) * binomial(5*n+3*k+3,n-k).