A371815 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-2*k-1,n-2*k).
1, 3, 20, 156, 1288, 10963, 95132, 836650, 7430956, 66501696, 598720080, 5416612336, 49201807276, 448442474938, 4099103160424, 37562606691526, 344959939645980, 3174051631201636, 29254814741949680, 270047153053464712, 2496167217049673468
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(4*n-2*k-1, n-2*k));
Formula
a(n) = [x^n] 1/((1+x^2) * (1-x)^(3*n)).
a(n) = binomial(4*n-1, n)*hypergeom([1, (1-n)/2, -n/2], [1/2-2*n, 1-2*n], -1). - Stefano Spezia, Apr 07 2024