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%I #21 Apr 16 2022 11:34:51
%S 0,48,768,4320,15360,42000,96768,197568,368640,641520,1056000,1661088,
%T 2515968,3690960,5268480,7344000,10027008,13441968,17729280,23046240,
%U 29568000,37488528,47021568,58401600,71884800,87750000,106299648,127860768,152785920,181454160
%N Molecular topological indices of the square graphs.
%H G. C. Greubel, <a href="/A192839/b192839.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = 8*n*(n+1)*(n-1)^3.
%F G.f.: 48*x^2*(1+x)*(1+9*x)/(1-x)^6. - _Colin Barker_, Aug 07 2012
%F E.g.f.: 8*x^2*(3 + 13*x + 8*x^2 + x^3)*exp(x). - _G. C. Greubel_, Jan 04 2019
%F From _Amiram Eldar_, Apr 16 2022: (Start)
%F Sum_{n>=2} 1/a(n) = 13/128 - Pi^2/64 + zeta(3)/16.
%F Sum_{n>=2} (-1)^n/a(n) = log(2)/4 - Pi^2/128 - 17/128 + 3*zeta(3)/64. (End)
%p [8*n*(n+1)*(n-1)^3$n=1..30]; # _Muniru A Asiru_, Jan 05 2019
%t Table[, {n,1,30}] (* _G. C. Greubel_, Jan 04 2019 *)
%o (PARI) vector(30, n, 8*n*(n+1)*(n-1)^3) \\ _G. C. Greubel_, Jan 04 2019
%o (Magma) [8*n*(n+1)*(n-1)^3: n in [1..30]]; // _G. C. Greubel_, Jan 04 2019
%o (Sage) [8*n*(n+1)*(n-1)^3 for n in (1..30)] # _G. C. Greubel_, Jan 04 2019
%o (GAP) List([1..30], n -> 8*n*(n+1)*(n-1)^3); # _G. C. Greubel_, Jan 04 2019
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Jul 11 2011
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