cp's OEIS Frontend

A386613 a(n) = Sum_{k=0..n-1} binomial(5*k,k) * binomial(5*n-5*k,n-k-1).

%I A386613 #19 Jul 29 2025 08:39:58
%S A386613 0,1,15,200,2570,32470,406411,5057440,62692100,775007135,9561421830,
%T A386613 117780193480,1449107627450,17811990468400,218768774024360,
%U A386613 2685209277718320,32940971570389960,403920568087927025,4950915045235523125,60663591616305306320,743092566613017730980,9100088494955802407060
%N A386613 a(n) = Sum_{k=0..n-1} binomial(5*k,k) * binomial(5*n-5*k,n-k-1).
%F A386613 G.f.: g^2 * (g-1)/(5-4*g)^2 where g=1+x*g^5.
%F A386613 G.f.: g/((1-g) * (1-5*g)^2) where g*(1-g)^4 = x.
%F A386613 a(n) = Sum_{k=0..n-1} binomial(5*k+l,k) * binomial(5*n-5*k-l,n-k-1) for every real number l.
%F A386613 a(n) = Sum_{k=0..n-1} 4^(n-k-1) * binomial(5*n+1,k).
%F A386613 a(n) = Sum_{k=0..n-1} 5^(n-k-1) * binomial(4*n+k+1,k).
%o A386613 (PARI) a(n) = sum(k=0, n-1, binomial(5*k, k)*binomial(5*n-5*k, n-k-1));
%Y A386613 Cf. A079678, A386367, A386566, A386614.
%Y A386613 Cf. A008549, A386611, A386615.
%K A386613 nonn
%O A386613 0,3
%A A386613 _Seiichi Manyama_, Jul 27 2025