A369128 Expansion of (1/x) * Series_Reversion( x / ((1+x)^5+x^5) ).

1, 5, 35, 285, 2530, 23752, 231910, 2331040, 23960235, 250692365, 2661086895, 28587333725, 310217791590, 3395464391870, 37442295427120, 415570885425280, 4638842010800025, 52044582325415025, 586553425250933055, 6637525235622842585, 75387741117556006435

Offset: 0

Author

Seiichi Manyama, Jan 14 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..924
• Index entries for reversions of series

Crossrefs

Cf. A071356, A192132, A369126.

Cf. A364522.

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+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)} binomial(n+1,k) * binomial(5*n-5*k+5,n-5*k).