A387117 a(n) = Sum_{k=0..n} binomial(3*n+k,n).

1, 7, 64, 589, 5396, 49259, 448876, 4088655, 37259596, 339893851, 3104834668, 28405204425, 260285994164, 2388895399804, 21959309034824, 202155838624275, 1863652690878588, 17203513487190059, 159002800228355860, 1471264394364089710, 13628234939950185720

Offset

0,2

Links

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

Formula

a(n) = binomial(4*n+1,n+1) - binomial(3*n,n+1).

Mathematica

Table[Sum[Binomial[3*n+k, n], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 20 2025 *)

Prog

(PARI) a(n) = binomial(4*n+1, n+1)-binomial(3*n, n+1);
(Magma) [&+[Binomial(3*n+k, n): k in [0..n]] : n in [0..25] ]; // Vincenzo Librandi, Dec 20 2025

Crossrefs

Cf. A108079, A391542.

Sequence in context: A159617 A098307 A055995 * A301424 A288690 A385514

Adjacent sequences: A387114 A387115 A387116 * A387118 A387119 A387120

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 13 2025

Status

approved