A296192 Denominators of the Harary index of the n X n grid graph.

1, 1, 6, 5, 28, 630, 396, 9009, 24024, 87516, 1511640, 5819814, 4576264, 106234700, 1147334760, 1890494775, 11031593040, 343817983080, 292314884400, 10274868186660

Offset

1,3

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 // Denominator
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

Crossrefs

Cf. A296191 (numerators).

Sequence in context: A267743 A298155 A219931 * A070399 A137763 A029763

Adjacent sequences: A296189 A296190 A296191 * A296193 A296194 A296195

Keyword

nonn,frac

Author

Eric W. Weisstein, Dec 07 2017

Status

approved