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Search: id:A002545
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| A002545 |
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Numerator of sum 1/(i*j*k) for i,j,k>0 and i+j+k=n.
(Formerly M2651 N1058)
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+0
2
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| 1, 3, 7, 15, 29, 469, 29531, 1303, 16103, 190553, 128977, 9061, 30946717, 39646461, 58433327, 344499373, 784809203, 169704792667, 665690574539, 5667696059, 337284946763, 7964656853269, 46951444927823, 284451446729
(list; graph; listen)
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OFFSET
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3,2
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COMMENT
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Numerators of coefficients for numerical differentiation.
sum(1/i*j*k for i,j,k>0 and i+j+k=n)=3*int(x^(n-1)*ln^2(x/(1-x)),x=0..1)-(Pi^2)/n [From Groux roland (roland.groux(AT)orange.fr), Nov 13 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
W. G. Bickley and J. C. P. Miller, Numerical differentiation near the limits of a difference table, Phil. Mag., 33 (1942), 1-12 (plus tables).
A. N. Lowan, H. E. Salzer and A. Hillman, A table of coefficients for numerical differentiation, Bull. Amer. Math. Soc., 48 (1942), 920-924.
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FORMULA
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G.f.: (-ln(1-x))^3 (for fractions A002545(n)/A002546(n))
A002545(n)/A002546(n)=6 stirling1(n+3, n)(-1)^n/(n+3)!
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MAPLE
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with(combinat):seq(numer(stirling1(j+3, 3)/(j+3)!*3!*(-1)^j), j=0..50);
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MATHEMATICA
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Table[Sum[1/i/j/(n-i-j), {i, n-2}, {j, n-i-1}], {n, 3, 100}] (Propper)
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CROSSREFS
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Cf. A002546.
Sequence in context: A120538 A146019 A147400 this_sequence A153114 A055795 A058695
Adjacent sequences: A002542 A002543 A002544 this_sequence A002546 A002547 A002548
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KEYWORD
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nonn,frac,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, GF, formula, Maple code from Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19, 2002
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