A390415 a(n) = Sum_{k=0..n} binomial(4*n+3*k+1,n-k).

1, 6, 49, 426, 3800, 34369, 313536, 2877073, 26512748, 245104797, 2271644202, 21096344235, 196244091617, 1828062312656, 17049031536276, 159166349907598, 1487264728073906, 13907980491243633, 130148776818166325, 1218664441160957790, 11417448252889419603

Offset

0,2

Links

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

Formula

G.f.: g/((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+1, n-k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 06 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*n+3*k+1, n-k));

Crossrefs

Cf. A257633, A386811, A390333, A390411, A390412, A390413, A390414, A390416.

Cf. A002293.

Sequence in context: A104170 A098306 A055847 * A388133 A371406 A365193

Adjacent sequences: A390412 A390413 A390414 * A390416 A390417 A390418

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2025

Status

approved