A378566 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+2*k-1,n-k).

1, 1, 9, 64, 465, 3456, 26082, 199060, 1532313, 11875015, 92528414, 724187982, 5689127886, 44834549501, 354289977750, 2806262293824, 22273793685609, 177113634045858, 1410633764438967, 11251419724586850, 89860413370562730, 718528004169570925

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A002002, A378565, A378567.

Cf. A052529, A362088, A365150.

Sequence in context: A049684 A037540 A037484 * A013566 A056769 A273232

Adjacent sequences: A378563 A378564 A378565 * A378567 A378568 A378569

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2024

Status

approved