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Search: id:A060944
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| A060944 |
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n!^2 * sum{k=1 to n} sum{j=1 to k}[1/j^2]. |
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+0
1
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| 1, 9, 130, 2900, 93576, 4141872, 241353792, 17929776384, 1655071418880, 185914776960000, 24978180045312000, 3955930130221056000, 729464836964806656000, 154952762244805582848000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,100
Leroy Quet, Home Page (listed in lieu of email address)
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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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
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EXAMPLE
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a(3) = 6^2 *(1 + (1 + 1/2^2) + (1 + 1/2^2 + 1/3^2)) = 130
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MATHEMATICA
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Table[(n!)^2*Sum[(k+1)/(n-k)^2, {k, 0, n-1}], {n, 1, 10}]
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PROGRAM
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(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]
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CROSSREFS
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Cf. A001705, A007406, A007407.
Sequence in context: A046754 A064746 A075762 this_sequence A112123 A167253 A097999
Adjacent sequences: A060941 A060942 A060943 this_sequence A060945 A060946 A060947
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet May 07 2001
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