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

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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

a(n) = Sum_{k=0..n} (-2)^k * binomial(4*n+k+1,n-k). - Seiichi Manyama, Nov 14 2025

Mathematica

Table[Sum[(-1)^k Binomial[4n-2k-1, n-2k], {k, 0, Floor[n/2]}], {n, 0, 20}] (* Harvey P. Dale, Oct 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(4*n-2*k-1, n-2*k));

Crossrefs

Cf. A225006, A262977, A371798.

Cf. A147855.

Sequence in context: A383897 A390571 A123355 * A258791 A192509 A336653

Adjacent sequences: A371812 A371813 A371814 * A371816 A371817 A371818

Keyword

nonn

Author

Seiichi Manyama, Apr 06 2024

Status

approved