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%I #9 Apr 16 2022 11:35:11
%S 0,0,0,6,60,300,1050,2940,7056,15120,29700,54450,94380,156156,248430,
%T 382200,571200,832320,1186056,1656990,2274300,3072300,4091010,5376756,
%U 6982800,8970000,11407500,14373450,17955756,22252860,27374550,33442800,40592640,48973056,58747920
%N a(n) = (n-3)*(n-2)^2*(n-1)^2*n/24.
%C Wiener index of the n-tetrahedral graph for n >= 6.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JohnsonGraph.html">Johnson Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralGraph.html">Tetrahedral Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WienerIndex.html">Wiener Index</a>.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = (n - 3)*(n - 2)^2*(n - 1)^2*n/24.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
%F G.f.: -6*x^4*(1 + 3*x + x^2)/(-1 + x)^7.
%F From _Amiram Eldar_, Apr 16 2022: (Start)
%F Sum_{n>=4} 1/a(n) = 119/3 - 4*Pi^2.
%F Sum_{n>=4} (-1)^n/a(n) = 67/3 - 32*log(2). (End)
%t Table[(n - 3) (n - 2)^2 (n - 1)^2 n/24, {n, 20}]
%t LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 6, 60, 300, 1050}, 20]
%t CoefficientList[Series[-((6 x^3 (1 + 3 x + x^2))/(-1 + x)^7), {x, 0, 20}], x]
%K nonn,easy
%O 1,4
%A _Eric W. Weisstein_, Sep 08 2017
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