id:A103930 - OEIS Search Results

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Numerators of squares of harmonic numbers A001008/A002805.

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1, 9, 121, 625, 18769, 2401, 131769, 579121, 50822641, 54479161, 7007531521, 7399612441, 1313299956049, 1372958223289, 1429834803049, 5936819760481, 1775966959381729, 203755669038601, 75787776947048401, 3117562300468225 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`The corresponding denominators are given in A103931.`
	LINKS	`W. Lang: Rationals H(n)^2.`
	FORMULA	`G.f.: -(diff((ln(1-x))^3, x))/3 + dilog(1-x)/(1-x) = ((ln(1-x)^2)+ dilog(1-x))/(1-x) with dilog(1-x)=polylog(2, x).` `First differences give A103932(n)/A103933(n).` `a(n)=numerator(H(n)^2), with the harmonic numbers H(n)=A001008(n)/A002805(n), n>=1.`
	CROSSREFS	`Sequence in context: A157930 A017102 A167722 this_sequence A138978 A046184 A084769` `Adjacent sequences: A103927 A103928 A103929 this_sequence A103931 A103932 A103933`
	KEYWORD	`nonn,easy,frac`
	AUTHOR	`Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Mar 24 2005`

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Last modified December 5 23:38 EST 2009. Contains 170428 sequences.

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