A368011 Expansion of (1/x) * Series_Reversion( x * ((1-x)^5-x^5) ).

1, 5, 40, 385, 4095, 46377, 548380, 6691620, 83637450, 1065311665, 13777916774, 180451354720, 2388503030675, 31900445734050, 429369814375480, 5818270533841408, 79309912829992350, 1086768622818959100, 14961519902879613700, 206839961042385226110

Offset: 0

Author

Seiichi Manyama, Jan 13 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369102, A369114.

Cf. A369125.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^5-x^5))/x)

PARI

a(n) = sum(k=0, n\5, binomial(n+k, k)*binomial(6*n+4, n-5*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} binomial(n+k,k) * binomial(6*n+4,n-5*k).