A386379 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/5)} a(5*k) * a(n-1-5*k).

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 13, 21, 30, 40, 51, 114, 190, 280, 385, 506, 1150, 1950, 2925, 4095, 5481, 12586, 21576, 32736, 46376, 62832, 145299, 250971, 383838, 548340, 749398, 1741844, 3025308, 4654320, 6690585, 9203634, 21475146, 37456650, 57887550

Offset: 0

Author

Seiichi Manyama, Jul 20 2025

Keywords

• nonn

Links

• Wikipedia, Fuss-Catalan number

Crossrefs

Cf. A002295, A212071, A212072, A212073, A130564.

Cf. A047749, A118968, A124753, A386380.

Programs

PARI

apr(n, p, r) = r*binomial(n*p+r, n)/(n*p+r);
a(n) = apr(n\5, 6, n%5+1);

Formula

For k=0..4, a(5*n+k) = (k+1) * binomial(6*n+k+1,n)/(6*n+k+1).

G.f. A(x) satisfies A(x) = 1/(1 - x * Product_{k=0..4} A(w^k*x)), where w = exp(2*Pi*i/5).