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Search: id:A001236
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| A001236 |
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Differences of reciprocals of unity.
(Formerly M4993 N2149)
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+0
3
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| 15, 575, 46760, 6998824, 1744835904, 673781602752, 381495483224064, 303443622431870976, 327643295527342080000, 466962174913357393920000, 858175477913267353681920000, 1993920215002599923346309120000
(list; graph; listen)
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OFFSET
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1,1
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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).
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
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FORMULA
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(n+1)!^3 * Sum[i=1..n+1, Sum[j=1..i, Sum[k=1..j, 1/(ijk) ]]].
a(n) = (n!^3/6)*(H(n, 1)^3+3*H(n, 1)*H(n, 2)+2*H(n, 3)), where H(n, m) = Sum_{i=1..n} 1/i^m are generalized harmonic numbers. a(n) = (n!^3/6)*((Psi(n+1)+gamma)^3+3*(Psi(n+1)+gamma)*(-Psi(1, n+1)+1/6*Pi^2)+Psi(2, n+1)+2*Zeta(3)). a(n) = n!^3*Sum_{k=1..n} (-1)^(k+1)*binomial(n, k)/k^3. Sum_{n>=0} a(n)*x^n/n!^3 = polylog(3, x/(x-1))/(x-1). (offset 2) - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 30 2005
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MAPLE
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a:= n-> (n+1)!^3* sum((-1)^(k+1) *binomial(n+1, k)/ k^3, k=1..n+1): seq (a(n), n=1..12); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 05 2008]
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CROSSREFS
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Column 3 in triangle A008969.
Cf. A000254, A000424, A001237, A001238.
Sequence in context: A012229 A027462 A027534 this_sequence A027505 A012210 A081022
Adjacent sequences: A001233 A001234 A001235 this_sequence A001237 A001238 A001239
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KEYWORD
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nonn
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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 from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 05 2008
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