A306753 a(n) = Sum_{k=0..n} binomial(k, 9*(n-k)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 11, 56, 221, 716, 2003, 5006, 11441, 24311, 48621, 92380, 167980, 294121, 498751, 824506, 1341154, 2177572, 3605251, 6249101, 11593726, 23138117, 48904469, 106653707, 234305936, 510034166, 1089810953, 2275676459, 4637090547

Offset: 0

Author

Seiichi Manyama, Mar 07 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3506
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1,1).

Crossrefs

Column 9 of A306680.

Cf. A017877.

Programs

Mathematica

a[n_] := Sum[Binomial[k, 9*(n-k)], {k, 0, n}]; Array[a, 38, 0] (* Amiram Eldar, Jun 21 2021 *)

PARI

{a(n) = sum(k=0, n, binomial(k, 9*(n-k)))}

PARI

N=66; x='x+O('x^N); Vec((1-x)^8/((1-x)^9-x^10))

Formula

G.f.: (1-x)^8/((1-x)^9 - x^10).

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) + a(n-10) for n > 9.

a(n) = A017877(9*n).