%I #8 Dec 09 2017 15:28:22
%S 0,5,133,293,3399,137111,140351,4854401,18690167,94423807,2190046361,
%T 11026443655,11090909287,323238388599,4312895221021,8658059232167,
%U 60805695015569,2256364094708093,2262227096103773,92967638570454913
%N Numerators 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 // Numerator
%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 // Numerator
%Y Cf. A296192 (denominators).
%K nonn,frac
%O 1,2
%A _Eric W. Weisstein_, Dec 07 2017