A390386 a(n) = Sum_{k=0..n} binomial(n+6*k,k).

1, 8, 100, 1445, 22146, 350302, 5652373, 92466885, 1527978234, 25444641278, 426305765326, 7177775060101, 121347548239251, 2058554309703855, 35023860868523405, 597395043712209100, 10212082517007883020, 174906856218730384677, 3000845130799132289494

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..700

Formula

G.f.: 1/((1-7*x*g^6) * (1-x*g)) where g = 1+x*g^7 is the g.f. of A002296.

a(n) ~ 7^(7*n + 13/2) / (109873 * sqrt(Pi*n) * 2^(6*n+1) * 3^(6*n + 1/2)). - Vaclav Kotesovec, Nov 04 2025

Mathematica

Table[Sum[Binomial[n+6*k, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 04 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+6*k, k));
(Magma) [&+[Binomial(n + 6*k, k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A002296, A186184, A390390.

Sequence in context: A261800 A208705 A246237 * A234513 A379024 A251686

Adjacent sequences: A390383 A390384 A390385 * A390387 A390388 A390389

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2025

Status

approved