A390339 - OEIS

%I #14 Nov 05 2025 08:44:28

%S 1,5,47,486,5249,58134,654514,7455031,85652055,990691064,11520294266,

%T 134551636752,1577237428486,18545745433881,218645029032749,

%U 2583630200233449,30590922143675921,362847559535088698,4310624876131037648,51282480944700740761,610871283295900453366

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

%H Vincenzo Librandi, <a href="/A390339/b390339.txt">Table of n, a(n) for n = 0..920</a>

%F 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.

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

%t Table[Sum[Binomial[5*n+k-1,n-k],{k,0,n}],{n,0,20}] (* _Vincenzo Librandi_, Nov 05 2025 *)

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

%Y Cf. A088305, A279014, A390337, A390338.

%Y Cf. A390332, A390334, A390336.

%Y Cf. A000045, A002294.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 01 2025