A369157 Expansion of (1/x) * Series_Reversion( x / ((1+x)^5-x^5) ).

1, 5, 35, 285, 2530, 23750, 231850, 2329850, 23940475, 250394375, 2656849375, 28529354375, 309445377750, 3385369628750, 37312228370000, 413913023212500, 4617886656665625, 51781448191328125, 583266654383859375, 6596645477096428125, 74881064169289121875

Offset: 0

Author

Seiichi Manyama, Jan 15 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A107264, A369156.

Cf. A349361, A369128.

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, (-1)^k*binomial(n+1, k)*binomial(5*n-5*k+5, n-5*k))/(n+1);

Formula

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