A371816 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(3*n-3*k-1,n-3*k).

1, 2, 10, 55, 322, 1947, 12013, 75154, 474946, 3024742, 19381045, 124797862, 806875421, 5234713031, 34060165282, 222174355575, 1452425614146, 9513309908589, 62418283102246, 410161124310550, 2698932409666237, 17781425199962255, 117281204608676426

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = [x^n] 1/((1+x^3) * (1-x)^(2*n)).

a(n) = binomial(3*n-1, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [1/3-n, 2/3-n, 1-n], -1). - Stefano Spezia, Apr 07 2024

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(3*n-3*k-1, n-3*k));

Crossrefs

Cf. A120305, A165817, A371817.

Cf. A371770.

Sequence in context: A202365 A330620 A268556 * A175935 A216721 A122826

Adjacent sequences: A371813 A371814 A371815 * A371817 A371818 A371819

Keyword

nonn

Author

Seiichi Manyama, Apr 06 2024

Status

approved