A390474 a(n) = Sum_{k=0..n} binomial(4*n+3*k+2,n-k).

1, 7, 59, 521, 4694, 42760, 392235, 3615130, 33435645, 310059105, 2881274034, 26819895379, 249997116279, 2333040203373, 21794367660851, 203770937428380, 1906640102047269, 17851921724990372, 167247225832972398, 1567702697372416423, 14702005735869692509

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^7)) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[Binomial[4*n+3*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+3*k+2, n-k));
(Magma) [&+[Binomial(4*n+3*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, A390473.

Cf. A002293.

Sequence in context: A359691 A218201 A015568 * A322667 A363105 A101487

Adjacent sequences: A390471 A390472 A390473 * A390475 A390476 A390477

Keyword

nonn

Author

Seiichi Manyama, Nov 06 2025

Status

approved