A371837 a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(2*n-3*k-1,n-3*k).

1, 1, 3, 13, 51, 201, 834, 3529, 15075, 65431, 288278, 1285263, 5799470, 26492103, 122432628, 572291385, 2705760291, 12937116213, 62542367166, 305668511259, 1510080076410, 7539381024297, 38034307340076, 193835252945487, 997724306958606, 5185731234177001

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

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

a(n) ~ exp(n^(2/3) + n^(1/3)/2 + 1/3) * n^(n/3) / 3. - Vaclav Kotesovec, Apr 08 2024

Mathematica

Join[{1}, Table[Sum[n^k*Binomial[2*n-3*k-1, n-1], {k, 0, n/3}], {n, 1, 25}]] (* Vaclav Kotesovec, Apr 08 2024 *)

Prog

(PARI) a(n) = sum(k=0, n\3, n^k*binomial(2*n-3*k-1, n-3*k));

Crossrefs

Cf. A293574, A371836.

Cf. A120305, A371827.

Sequence in context: A370272 A304629 A301458 * A244784 A197074 A014985

Adjacent sequences: A371834 A371835 A371836 * A371838 A371839 A371840

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2024

Status

approved