A390339 a(n) = Sum_{k=0..n} binomial(5*n+k-1,n-k).

1, 5, 47, 486, 5249, 58134, 654514, 7455031, 85652055, 990691064, 11520294266, 134551636752, 1577237428486, 18545745433881, 218645029032749, 2583630200233449, 30590922143675921, 362847559535088698, 4310624876131037648, 51282480944700740761, 610871283295900453366

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..920

Formula

G.f.: 1/(g * (1-5*x*g^4) * (1-x*g^6)) where g = 1+x*g^5 is the g.f. of A002294.

a(n) = Sum_{k=0..n} binomial(5*n-1,n-k) * Fibonacci(k+1).

Mathematica

Table[Sum[Binomial[5*n+k-1, n-k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 05 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(5*n+k-1, n-k));

Crossrefs

Cf. A088305, A279014, A390337, A390338.

Cf. A390332, A390334, A390336.

Cf. A000045, A002294.

Sequence in context: A241372 A124267 A388531 * A124450 A136023 A370100

Adjacent sequences: A390336 A390337 A390338 * A390340 A390341 A390342

Keyword

nonn

Author

Seiichi Manyama, Nov 01 2025

Status

approved