A371776 a(n) = Sum_{k=0..floor(n/3)} binomial(5*n-k+1,n-3*k).
1, 6, 55, 561, 6005, 66080, 740342, 8400074, 96206994, 1109874635, 12877808194, 150122945518, 1756887201266, 20628519611407, 242891806678851, 2866906127955287, 33910670558191711, 401857349039547372, 4770115555036932777, 56706219260783415643
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[Binomial[5n-k+1,n-3k],{k,0,Floor[n/3]}],{n,0,20}] (* Harvey P. Dale, May 13 2025 *) -
PARI
a(n) = sum(k=0, n\3, binomial(5*n-k+1, n-3*k));
Formula
a(n) = [x^n] 1/(((1-x)^2-x^3) * (1-x)^(4*n)).