A390411 a(n) = Sum_{k=0..n} binomial(4*k+1,k).

1, 6, 42, 328, 2708, 23057, 200157, 1760937, 15645093, 140048713, 1261148121, 11411744031, 103675478867, 945068445337, 8639713141537, 79179700984057, 727225637926357, 6691946005587313, 61683628785361697, 569433512890810297, 5263869701729927017

Offset

0,2

Links

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

Formula

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

a(n) ~ 2^(8*n + 21/2) / (229 * sqrt(Pi*n) * 3^(3*n + 3/2)). - Vaclav Kotesovec, Nov 05 2025

Mathematica

Table[Sum[Binomial[4*k+1, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 05 2025 *)

Prog

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

Crossrefs

Partial sums of A052203.

Cf. A257633, A386811, A390333, A390412, A390413, A390414, A390415, A390416.

Cf. A002293, A225612.

Sequence in context: A118351 A033296 A364437 * A218755 A165314 A082302

Adjacent sequences: A390408 A390409 A390410 * A390412 A390413 A390414

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2025

Status

approved