A365754 Expansion of (1/x) * Series_Reversion( x*(1-x)/(1+x)^4 ).

1, 5, 36, 305, 2833, 27916, 286632, 3033513, 32858595, 362515725, 4059475368, 46021411644, 527163783916, 6092053249160, 70939443268112, 831558454663449, 9804617762941095, 116201796106426543, 1383557994261012100, 16541672701743657545, 198510770031798279825

Offset: 0

Author

Seiichi Manyama, Sep 18 2023

Keywords

• nonn

Crossrefs

Cf. A000108, A006318, A107111, A263843, A365755.

Cf. A365752.

Programs

PARI

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

Formula

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

a(n) = (1/(n+1)) * [x^n] ( (1+x)^4 / (1-x) )^(n+1). - Seiichi Manyama, Feb 17 2024