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
Keywords
Links
- Wikipedia, Fuss-Catalan number
Programs
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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).