A365753 Expansion of (1/x) * Series_Reversion( x*(1+x)*(1-x)^5 ).

1, 4, 27, 220, 1984, 19064, 191325, 1981932, 21031965, 227463808, 2498039219, 27782561352, 312281382836, 3541879743840, 40484779373060, 465888833819532, 5393215780225983, 62761359573224612, 733784067570047400, 8615217370731224160, 101533102164551821896

Offset: 0

Author

Seiichi Manyama, Sep 18 2023

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A063020, A365751, A365752.

Cf. A365755.

Programs

PARI

a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(6*n-k+4, n-k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(n+k,k) * binomial(6*n-k+4,n-k).

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+k,k) * binomial(5*n-2*k+3,n-2*k). - Seiichi Manyama, Jan 18 2024

a(n) = (1/(n+1)) * [x^n] 1/( (1+x) * (1-x)^5 )^(n+1). - Seiichi Manyama, Feb 16 2024