A390358 a(n) = Sum_{k=0..n} binomial(3*n+2*k,n-k).

1, 4, 24, 153, 998, 6586, 43761, 292060, 1955130, 13116793, 88142646, 593041755, 3993997033, 26919539964, 181551848888, 1225061008029, 8269904756032, 55846867568653, 377249292917109, 2548999356721459, 17226879374556972, 116446327805377871, 787256381742222535

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1/((1-3*x*g^2) * (1-x*g^5)) where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[Binomial[3* n+2*k, n-k], {k, 0, n}], {n, 0, 28}] (* Vincenzo Librandi, Jan 03 2026 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(3*n+2*k, n-k));
(Magma) [&+[Binomial(3*n + 2*k, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A038736, A045721, A066380, A188675, A388043, A390359.

Cf. A052544, A360143.

Cf. A001764.

Sequence in context: A262407 A192927 A003288 * A178879 A091166 A078108

Adjacent sequences: A390355 A390356 A390357 * A390359 A390360 A390361

Keyword

nonn

Author

Seiichi Manyama, Nov 02 2025

Status

approved