A383526 a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n-2*k,k)^2.

1, 1, 1, 4, 17, 46, 112, 365, 1297, 4126, 12686, 41647, 141440, 470887, 1553021, 5205769, 17665105, 59858038, 202599814, 689183087, 2355887902, 8065291637, 27637715887, 94924591313, 326810899744, 1126888746871, 3890420726167, 13450563963085, 46571447873597

Offset: 0

Author

Seiichi Manyama, Apr 29 2025

Keywords

• nonn

Comments

Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - x*y^3*z^3).

Crossrefs

Cf. A000172, A248658, A383525.

Programs

PARI

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