A387745 a(n) = (1/6) * Sum_{k=0..n-1} binomial(6*n,6*k+1).

0, 1, 134, 6735, 480796, 29427581, 1919636034, 121877393275, 7826594617976, 500188136444361, 32031316548303934, 2049483812063101415, 131181016041803950356, 8395205620791785408341, 537303403689533286323834, 34387141249240936779595155, 2200784507797428179612605936

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (38,1691,-1728).

Formula

a(n) = (1/6) * Sum_{k=0..n-1} binomial(6*n,6*k+5).

G.f.: x * (1+96*x-48*x^2)/((1-64*x) * (1-x) * (1+27*x)).

a(n) = 38*a(n-1) + 1691*a(n-2) - 1728*a(n-3) for n > 3.

E.g.f.: (exp(64*x) + exp(-27*x) - exp(-x) - 1)/36. - Stefano Spezia, Sep 07 2025

Mathematica

Table[(1/6)*Sum[Binomial[6*n, 6*k+1], {k, 0, n-1}], {n, 0, 14}] (* Vincenzo Librandi, Sep 08 2025 *)

Prog

(PARI) a(n) = sum(k=0, n-1, binomial(6*n, 6*k+1))/6;
(Magma) [&+[(1/6)* Binomial(6*n, 6*k+1): k in [0..n]]: n in [0..15]]; // Vincenzo Librandi, Sep 08 2025

Crossrefs

Cf. A015565, A387743, A387748, A387751, A387752, A387753, A387754.

Cf. A070967, A387746, A387747.

Sequence in context: A370162 A007251 A219443 * A348815 A230699 A374536

Adjacent sequences: A387742 A387743 A387744 * A387746 A387747 A387748

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 06 2025

Status

approved