A391778 - OEIS

%I #10 Jan 08 2026 02:50:25

%S 0,0,1,16,120,640,2800,10752,37632,122880,380160,1126400,3221504,

%T 8945664,24227840,64225280,167116800,427819008,1079574528,2689597440,

%U 6624378880,16148070400,38997590016,93381984256,221878681600,523449139200,1226833920000,2858032300032

%N a(n) = n*(n-1)*(n- 2)^2*2^(n-4)/3.

%C Also the number of tetrahedra in the halved cube graph Q_n/2.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphTetrahedron.html">Graph Tetrahedron</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HalvedCubeGraph.html">Halved Cube Graph</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,80,-80,32).

%F a(n) = 10*a(n-1)-40*a(n-2)+80*a(n-3)-80*a(n-4)+32*a(n-5).

%F G.f.: -x^3*(1+6*x)/(-1+2*x)^5.

%F Sum_{n>=3} 1/a(n) = Pi^2/2 + 3*log(2)*(1-log(2)) - 9/2. - _Amiram Eldar_, Jan 08 2026

%t Table[n (n - 1) (n - 2)^2 2^(n - 4)/3, {n, 28}]

%t LinearRecurrence[{10, -40, 80, -80, 32}, {0, 0, 1, 16, 120, 640}, 20]

%t CoefficientList[Series[x^2 (1 + 6 x)/(1 - 2 x)^5, {x, 0, 20}], x]

%K nonn,easy

%O 1,4

%A _Eric W. Weisstein_, Dec 19 2025