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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
OFFSET
1,2
LINKS
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 A344395 A280305
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Dec 07 2017
STATUS
approved