A390268 - OEIS

%I #11 Nov 04 2025 12:37:32

%S 1,4,19,94,470,2357,11829,59368,297902,1494469,7495425,37584962,

%T 188432209,944567955,4734350650,23727223169,118905239428,595839590228,

%U 2985639571718,14959922129662,74956381227810,375558759884508,1881652000369616,9427455976971208,47232924151619828

%N a(n) = Sum_{k=0..n} binomial(2*n+3*k+1,n-k).

%H Vincenzo Librandi, <a href="/A390268/b390268.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: c(x)/( sqrt(1-4*x) * (1-x*c(x)^5) ), where c(x) is the g.f. of A000108.

%t Table[Sum[Binomial[2*n+3*k+1,n-k],{k,0,n}],{n,0,30}] (* _Vincenzo Librandi_, Nov 04 2025 *)

%o (PARI) a(n) = sum(k=0, n, binomial(2*n+3*k+1, n-k));

%Y Cf. A000302, A001791, A079309, A390266, A390267.

%Y Cf. A000108, A360144.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 30 2025