A390390 a(n) = Sum_{k=0..n} binomial(n+6*k+6,k).

1, 14, 205, 3151, 49900, 805683, 13185440, 217944999, 3630071774, 60828674720, 1024308923595, 17318722238090, 293821332117924, 4999371409794830, 85278371776537055, 1457853685496849330, 24970424288537691279, 428429908698284040067, 7361999473607086841901

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..800

Formula

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

Mathematica

Table[Sum[Binomial[n+6*k+6, k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+6*k+6, k));

Crossrefs

Cf. A002296, A186184, A390386.

Sequence in context: A068769 A113349 A109764 * A349283 A333949 A002961

Adjacent sequences: A390387 A390388 A390389 * A390391 A390392 A390393

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2025

Status

approved