A366052 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1-x+x^3) ).

1, 2, 7, 31, 154, 819, 4559, 26226, 154664, 930040, 5680920, 35150493, 219850505, 1387717660, 8828668582, 56553846890, 364449091112, 2361118198094, 15369247139879, 100468188756849, 659271433474584, 4341140182940382, 28675590236716905

Offset: 0

Author

Seiichi Manyama, Sep 27 2023

Keywords

• nonn

Crossrefs

Cf. A049128, A114997, A366051, A366053.

Programs

PARI

a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(3*n-2*k+1, n-3*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(3*n-2*k+1,n-3*k).