A390473 a(n) = Sum_{k=0..n} binomial(4*n+2*k+2,n-k).

1, 7, 58, 503, 4456, 39969, 361473, 3288412, 30048831, 275540020, 2533770713, 23354149592, 215682938096, 1995259922665, 18484932381034, 171471766047681, 1592427393435786, 14803545258192952, 137741955609776899, 1282694585997734148, 11953754045310086497

Offset

0,2

Links

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

Formula

G.f.: g^2/((1-4*x*g^3) * (1-x*g^6)) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[Binomial[4*n+2*k+2, n-k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n+2*k+2, n-k));
(Magma) [&+[Binomial(4*n+2*k+2, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 08 2025

Crossrefs

Cf. A224274, A387009, A389471, A390335, A390471, A390472, A390474.

Cf. A002293.

Sequence in context: A015566 A238810 A385605 * A362210 A334610 A383601

Adjacent sequences: A390470 A390471 A390472 * A390474 A390475 A390476

Keyword

nonn

Author

Seiichi Manyama, Nov 06 2025

Status

approved