A390711 - OEIS

%I #11 Nov 17 2025 09:25:38

%S 1,2,9,59,464,4036,37394,361752,3611342,36924037,384695774,4069309941,

%T 43587515276,471807637123,5152872105955,56712277598154,

%U 628369045481689,7003390219941228,78462945395340756,883157697492760759,9982097511692809864,113250010579766749951

%N a(n) = Sum_{k=0..n} (2*k+1) * binomial(5*n-3*k+1,n-k)/(5*n-3*k+1).

%H Vincenzo Librandi, <a href="/A390711/b390711.txt">Table of n, a(n) for n = 0..920</a>

%F G.f.: g/(1-x*g^2) where g = 1+x*g^5 is the g.f. of A002294.

%t Table[Sum[(2*k+1)*Binomial[5*n-3*k+1,n-k]/(5*n-3*k+1),{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Nov 17 2025 *)

%o (PARI) a(n) = sum(k=0, n, (2*k+1)*binomial(5*n-3*k+1, n-k)/(5*n-3*k+1));

%o (Magma) [&+[(2*k+1)*Binomial(5*n-3*k+1, n-k)/(5*n-3*k+1): k in [0..n]] : n in [0..30] ]; // _Vincenzo Librandi_, Nov 17 2025

%Y Cf. A118969, A304979, A390712.

%Y Cf. A002294.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 15 2025