OFFSET
1,5
LINKS
Eric Weisstein's World of Mathematics, Harmonic Number
FORMULA
G.f. of column k: PolyLog(k,x)/(1 - x), where PolyLog() is the polylogarithm function (for rationals Sum_{j=1..n} 1/j^k).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
2, 3/2, 5/4, 9/8, 17/16, ...
3, 11/6, 49/36, 251/216, 1393/1296, ...
4, 25/12, 205/144, 2035/1728, 22369/20736, ...
5, 137/60, 5269/3600, 256103/216000, 14001361/12960000, ...
MATHEMATICA
Table[Function[k, Denominator[Sum[1/j^k, {j, 1, n}]]][i - n], {i, 0, 10}, {n, 1, i}] // Flatten
Table[Function[k, Denominator[HarmonicNumber[n, k]]][i - n], {i, 0, 10}, {n, 1, i}] // Flatten
Table[Function[k, Denominator[SeriesCoefficient[PolyLog[k, x]/(1 - x), {x, 0, n}]]][i - n], {i, 0, 10}, {n, 1, i}] // Flatten
CROSSREFS
KEYWORD
AUTHOR
Ilya Gutkovskiy, Dec 01 2018
STATUS
approved