A390383 a(n) = Sum_{k=0..n} binomial(n+3*k+3,k).

1, 8, 64, 531, 4525, 39277, 345433, 3067863, 27452622, 247134150, 2235610238, 20305403848, 185055810669, 1691427324498, 15498568922011, 142324124371044, 1309483858158145, 12068738732981817, 111399782220575993, 1029675188344765864, 9529104863113503460

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: g^3/((1-4*x*g^3) * (1-x*g)) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[Binomial[n+3*k+3, k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+3*k+3, k));

Crossrefs

Cf. A002293, A130458, A389239.

Sequence in context: A245852 A033144 A238300 * A344271 A144317 A344054

Adjacent sequences: A390380 A390381 A390382 * A390384 A390385 A390386

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2025

Status

approved