Search: id:A060944
Results 1-1 of 1 results found.

%I A060944
%S A060944 1,9,130,2900,93576,4141872,241353792,17929776384,1655071418880,
%T A060944 185914776960000,24978180045312000,3955930130221056000,
%U A060944 729464836964806656000,154952762244805582848000
%N A060944 n!^2 * sum{k=1 to n} sum{j=1 to k}[1/j^2].
%C A060944 Sum of generalized harmonic numbers squared multiplied by (n!)^2. a(n) 
               = Sum[HarmonicNumber[k, 2]], k = 1..n, where HarmonicNumber[k, 2] 
               = Sum[1/k^2], k = 1..n. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Oct 27 2004
%H A060944 Harry J. Smith, <a href="b060944.txt">Table of n, a(n) for n=1,...,100</
               a>
%H A060944 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%H A060944 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HarmonicNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A060944 a(n) = (n!)^2 * Sum[(k+1)/(n-k)^2, {k, 0, n-1}], a(n) = (n!)^2 * Sum[HarmonicNumber[k, 
               2]], {k, 1, n}], HarmonicNumber[k, 2] = A007406(k) / A007407(k). 
               - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 27 2004
%e A060944 a(3) = 6^2 *(1 + (1 + 1/2^2) + (1 + 1/2^2 + 1/3^2)) = 130
%t A060944 Table[(n!)^2*Sum[(k+1)/(n-k)^2, {k, 0, n-1}], {n, 1, 10}]
%o A060944 (PARI) { default(realprecision, 100); for (n=1, 100, write("b060944.txt", 
               n, " ", n!^2 * sum(k=1, n, sum(j=1, k, 1/j^2))); ) } [From Harry 
               J. Smith (hjsmithh(AT)sbcglobal.net), Jul 15 2009]
%Y A060944 Cf. A001705, A007406, A007407.
%Y A060944 Sequence in context: A046754 A064746 A075762 this_sequence A112123 A167253 
               A097999
%Y A060944 Adjacent sequences: A060941 A060942 A060943 this_sequence A060945 A060946 
               A060947
%K A060944 easy,nonn
%O A060944 1,2
%A A060944 Leroy Quet May 07 2001

Search completed in 0.001 seconds