A371817 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(4*n-3*k-1,n-3*k).
1, 3, 21, 164, 1353, 11508, 99808, 877425, 7790745, 69704921, 627438606, 5675535000, 51546958296, 469764721533, 4293594852225, 39341599326304, 361271345551257, 3323924166943410, 30634431485945569, 282767849049333909, 2613630939017216898
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, (-1)^k*binomial(4*n-3*k-1, n-3*k));
Formula
a(n) = [x^n] 1/((1+x^3) * (1-x)^(3*n)).
a(n) = binomial(4*n-1, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [(1-4*n)/3, (2-4*n)/3, 1-4*n/3], -1). - Stefano Spezia, Apr 07 2024