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Search: id:A098107
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| A098107 |
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Sum of all matrix elements M(i,j) = n!*(i/j), (i,j = 1..n). |
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1
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| 1, 9, 66, 500, 4110, 37044, 365904, 3945024, 46195920, 584575200, 7955893440, 115942544640, 1802051072640, 29763892972800, 520699560192000, 9619862405529600, 187181055358617600, 3826464958007193600
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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!*Sum[Sum[(i/j), {i, 1, n}], {j, 1, n}]
a(n) = (-1)^(n+1)*(n*(n+1)/2)*Stirling1(n+1, 2). E.g.f.: x*(x+2-2*ln(1-x))/(2*(1-x)^3). - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 09 2004
a(n) = n! * T(n) * H(n), where T(n) = n(n+1)/2 is triangular number A000217(n) and H(n) = Sum(1/i) (i=1..n) is harmonic number A001008(n)/A002805(n). - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 09 2004
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EXAMPLE
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a(2) = 2! * (1/1 + 2/1 + 1/2 + 2/2) = 9
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MATHEMATICA
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Table[n!*Sum[Sum[(i/j), {i, 1, n}], {j, 1, n}], {n, 1, 20}]
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CROSSREFS
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Cf. A000217, A001008, A002805, A000254.
Sequence in context: A014830 A048439 A134432 this_sequence A091647 A106132 A105287
Adjacent sequences: A098104 A098105 A098106 this_sequence A098108 A098109 A098110
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 24 2004
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