

A296191


Numerators of the Harary index of the n X n grid graph.


1



0, 5, 133, 293, 3399, 137111, 140351, 4854401, 18690167, 94423807, 2190046361, 11026443655, 11090909287, 323238388599, 4312895221021, 8658059232167, 60805695015569, 2256364094708093, 2262227096103773, 92967638570454913
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..20.
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Harary Index


EXAMPLE

0, 5, 133/6, 293/5, 3399/28, 137111/630, 140351/396, ...


MATHEMATICA

Table[n (2 n + 1) (2 + (2 n  1) Derivative[1][Log[CatalanNumber[#  1]] &][n]  n)/3, {n, 20}] // FullSimplify // Numerator
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


CROSSREFS

Cf. A296192 (denominators).
Sequence in context: A135758 A152794 A053517 * A114474 A280305 A085506
Adjacent sequences: A296188 A296189 A296190 * A296192 A296193 A296194


KEYWORD

nonn,frac


AUTHOR

Eric W. Weisstein, Dec 07 2017


STATUS

approved



