A390388 a(n) = Sum_{k=0..n} binomial(n+4*k+4,k).

1, 10, 102, 1086, 11899, 132885, 1504068, 17193516, 198048061, 2295079168, 26727127205, 312513034302, 3666620879703, 43144771987875, 508957616798605, 6017090458256401, 71273551528056549, 845691881456979030, 10049815922281625560, 119591059353652383362, 1424873411908463345057

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Formula

G.f.: g^4/((1-5*x*g^4) * (1-x*g)) where g = 1+x*g^5 is the g.f. of A002294.

Mathematica

Table[Sum[Binomial[n+4*k+4, k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+4*k+4, k));

Crossrefs

Cf. A002294, A186182, A390384.

Sequence in context: A191014 A147550 A162666 * A061630 A062806 A336952

Adjacent sequences: A390385 A390386 A390387 * A390389 A390390 A390391

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2025

Status

approved