A387752 a(n) = (1/9) * Sum_{k=0..n-1} binomial(9*n,9*k+1).

0, 1, 4864, 1184043, 986882648, 393870724604, 234248236477968, 110403059561827081, 59314586154397503577, 29553482672024441950476, 15369950884066398872755703, 7799631141982301532176946782, 4013823652653051097310367754494, 2049106825578573532208804624821984

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..250

Index entries for linear recurrences with constant coefficients, signature (265,139823,-6826204,-6965249,512).

Formula

a(n) = (1/9) * Sum_{k=0..n-1} binomial(9*n,9*k+8).

G.f.: x * (1+4599*x-244740*x^2-161615*x^3)/((1-512*x) * (1+x) * (1+246*x-13605*x^2+x^3)).

a(n) = 265*a(n-1) + 139823*a(n-2) - 6826204*a(n-3) - 6965249*a(n-4) + 512*a(n-5) for n > 4.

Mathematica

Table[(1/9)*Sum[Binomial[9*n, 9*k+1], {k, 0, n-1}], {n, 0, 14}] (* Vincenzo Librandi, Sep 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n-1, binomial(9*n, 9*k+1))/9;
(Magma) [&+[(1/9)* Binomial(9*n, 9*k+1): k in [0..n]]: n in [0..15]]; // Vincenzo Librandi, Sep 07 2025

Crossrefs

Cf. A015565, A387743, A387745, A387748, A387751, A387753, A387754.

Cf. A094213.

Sequence in context: A321978 A147697 A208629 * A272077 A259329 A390773

Adjacent sequences: A387749 A387750 A387751 * A387753 A387754 A387755

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 06 2025

Status

approved