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%I #7 Dec 09 2017 15:28:13
%S 1,1,6,5,28,630,396,9009,24024,87516,1511640,5819814,4576264,
%T 106234700,1147334760,1890494775,11031593040,343817983080,
%U 292314884400,10274868186660
%N Denominators of the Harary index of the n X n grid graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HararyIndex.html">Harary Index</a>
%e 0, 5, 133/6, 293/5, 3399/28, 137111/630, 140351/396, ...
%t Table[n (2 n + 1) (2 + (2 n - 1) Derivative[1][Log[CatalanNumber[# - 1]] &][n] - n)/3, {n, 20}] // FullSimplify // Denominator
%t Table[n (2 n + 1) (2 + (2 n - 1) (HarmonicNumber[n - 3/2] - HarmonicNumber[n] + 2 Log[2]) - n)/3, {n, 20}] // FunctionExpand // FullSimplify // Denominator
%Y Cf. A296191 (numerators).
%K nonn,frac
%O 1,3
%A _Eric W. Weisstein_, Dec 07 2017
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