A390966 - OEIS

%I #15 Dec 06 2025 06:38:20

%S 0,1,10,56,258,1089,4394,17290,67048,257754,985796,3759074,14311750,

%T 54452385,207163530,788414010,3002300400,11441617950,43641721260,

%U 166619689080,636761192964,2435899184922,9327702931140,35753497006596,137177675480048,526817306712340

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

%H Vincenzo Librandi, <a href="/A390966/b390966.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: x*g^6 * (1 + 4*x*g + x^2*g^2), where g = 1+x*g^2 is the g.f. of A000108.

%t Table[Sum[k^3*(k+1)*Binomial[2*n-k,n-k]/(n+1),{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Dec 06 2025 *)

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

%o (Magma) [&+[k^3*(k+1)*Binomial(2*n-k, n-k)/(n+1): k in [0..n]] : n in [0..30] ]; // _Vincenzo Librandi_, Dec 06 2025

%Y Cf. A390965, A390967.

%Y Cf. A000108.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 25 2025