A370844 Expansion of (1/x) * Series_Reversion( x / (1/(1-x)^4 + x) ).

1, 5, 35, 295, 2760, 27556, 287564, 3098780, 34216020, 385106280, 4401850866, 50957904938, 596231618166, 7039674475190, 83767631913840, 1003564049999916, 12094813260406732, 146534778450346908, 1783695235540931924, 21803615393276536720, 267537602528379374851

Offset: 0

Author

Seiichi Manyama, Mar 03 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A007317, A369616, A369617.

Cf. A118971.

Programs

PARI

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

PARI

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

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A118971(k).

a(n) = hypergeom([4/5, 6/5, 7/5, 8/5, -n], [5/4, 3/2, 7/4, 2], -3125/256). - Stefano Spezia, Mar 03 2024