A383572 Expansion of 1/sqrt((1-x^4)^2 - 4*x^5).

1, 0, 0, 0, 1, 2, 0, 0, 1, 6, 6, 0, 1, 12, 30, 20, 1, 20, 90, 140, 71, 30, 210, 560, 631, 294, 420, 1680, 3151, 2828, 1680, 4200, 11551, 16704, 13272, 12672, 34651, 72162, 86064, 69960, 102961, 252362, 423390, 446160, 429001, 805508, 1685970, 2393820, 2419561

Offset: 0

Author

Seiichi Manyama, Apr 30 2025

Keywords

• nonn

Comments

Number of lattice paths from (0,0) to (n,n) using steps (5,0),(0,5),(4,4).

Diagonal of the rational function 1 / (1 - x^5 - y^5 - x^4*y^4).

Crossrefs

Cf. A002426, A182883, A383571.

Cf. A376792.

Programs

PARI

a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(k, n-4*k));

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(k,n-4*k).