A390413 a(n) = Sum_{k=0..n} binomial(4*n-2*k+1,n-k).

1, 6, 44, 351, 2925, 25024, 217855, 1920294, 17084132, 153086649, 1379651559, 12491989470, 113548602181, 1035517749804, 9470070234115, 86816958616031, 797587813229949, 7341174862067839, 67682231788525816, 624926911642533285, 5777822809966547699

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^2)) where g = 1+x*g^4 is the g.f. of A002293.

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

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-k+2,n-2*k).

Mathematica

Table[Sum[Binomial[4*n-2*k+1, 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+1, n-k));

Crossrefs

Cf. A257633, A386811, A390333, A390411, A390412, A390414, A390415, A390416.

Cf. A371786, A390407, A390472.

Cf. A002293.

Sequence in context: A082412 A108452 A363104 * A005591 A052204 A147688

Adjacent sequences: A390410 A390411 A390412 * A390414 A390415 A390416

Keyword

nonn

Author

Seiichi Manyama, Nov 04 2025

Status

approved