A390389 a(n) = Sum_{k=0..n} binomial(n+5*k+5,k).

1, 12, 149, 1938, 25961, 354543, 4907672, 68612316, 966594646, 13699722770, 195123252547, 2790416145428, 40041643612330, 576261707599940, 8314178569828744, 120218343265376255, 1741643652412794091, 25274928742533804784, 367352410122031305318, 5346512752425236662435

Offset

0,2

Links

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

Formula

G.f.: g^5/((1-6*x*g^5) * (1-x*g)) where g = 1+x*g^6 is the g.f. of A002295.

Mathematica

Table[Sum[Binomial[n+5*k+5, k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+5*k+5, k));

Crossrefs

Cf. A002295, A186183, A390385.

Sequence in context: A057572 A114106 A015610 * A141326 A154733 A305544

Adjacent sequences: A390386 A390387 A390388 * A390390 A390391 A390392

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2025

Status

approved