A387750 a(n) = (1/7) * Sum_{k=0..n-1} binomial(7*n,7*k+3).

0, 5, 195, 51433, 4945863, 734061693, 87730167995, 11613740867393, 1462854616670751, 188707581658599477, 24064375447320971379, 3085803721956167224409, 394639682628293253732919, 50535049230904047059165869, 6467180442410853831882517483, 827879648344598212869192726577

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (71,7585,-36991,-128).

Formula

a(n) = (1/7) * Sum_{k=0..n-1} binomial(7*n,7*k+4).

G.f.: x * (5-160*x-337*x^2)/((1-128*x) * (1+57*x-289*x^2-x^3)).

a(n) = 71*a(n-1) + 7585*a(n-2) - 36991*a(n-3) - 128*a(n-4) for n > 3.

Mathematica

Table[(1/7)*Sum[Binomial[7*n, 7*k+3], {k, 0, n-1}], {n, 0, 18}] (* Vincenzo Librandi, Sep 09 2025 *)

Prog

(PARI) a(n) = sum(k=0, n-1, binomial(7*n, 7*k+3))/7;
(Magma) [&+[(1/7)* Binomial(7*n, 7*k+3): k in [0..n]]: n in [0..19]]; // Vincenzo Librandi, Sep 09 2025

Crossrefs

Cf. A094211, A387748, A387749.

Sequence in context: A194573 A194574 A194575 * A240772 A142927 A114351

Adjacent sequences: A387747 A387748 A387749 * A387751 A387752 A387753

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 06 2025

Status

approved