A390335 a(n) = Sum_{k=0..n} binomial(4*n+k+2,n-k).

1, 7, 57, 486, 4241, 37540, 335556, 3020993, 27348189, 248663695, 2269092254, 20767746644, 190557813508, 1752306266909, 16144180450517, 148985760946626, 1376936590378553, 12742505309329660, 118061810775750705, 1095036012738747487, 10166448485964693086

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^5)) where g = 1+x*g^4 is the g.f. of A002293.

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

Mathematica

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

Crossrefs

Cf. A027941, A390238, A390336.

Cf. A389361, A390333, A390338.

Cf. A000045, A002293.

Sequence in context: A015565 A349303 A268316 * A291537 A082413 A142990

Adjacent sequences: A390332 A390333 A390334 * A390336 A390337 A390338

Keyword

nonn

Author

Seiichi Manyama, Nov 01 2025

Status

approved