A390336 a(n) = Sum_{k=0..n} binomial(5*n+k+2,n-k).

1, 8, 80, 853, 9388, 105326, 1197117, 13734865, 158715688, 1844434121, 21532145438, 252318496636, 2966118233525, 34962580152413, 413079890597081, 4890475172075789, 58002772328563708, 689032048554462015, 8196897079857382577, 97637481503956569960, 1164360218222146935142

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..918

Formula

G.f.: g^2/((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+2,n-k) * Fibonacci(k+1).

Mathematica

Table[Sum[Binomial[5*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(5*n+k+2, n-k));

Crossrefs

Cf. A027941, A390238, A390335.

Cf. A390332, A390334, A390339.

Cf. A000045, A002294.

Sequence in context: A136949 A346178 A102592 * A345081 A320759 A233123

Adjacent sequences: A390333 A390334 A390335 * A390337 A390338 A390339

Keyword

nonn

Author

Seiichi Manyama, Nov 01 2025

Status

approved