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A000424
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Differences of reciprocals of unity.
(Formerly M4448 N1883)
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4
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7, 85, 1660, 48076, 1942416, 104587344, 7245893376, 628308907776, 66687811660800, 8506654697548800, 1284292319599411200, 226530955276874956800, 46165213716463676620800, 10765453901922078105600000, 2848453606917036402278400000, 848800150518516674081587200000
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OFFSET
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1,1
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..16.
Mircea Merca, Some experiments with complete and elementary symmetric functions, Periodica Mathematica Hungarica, 69 (2014), 182-189.
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FORMULA
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From Vaclav Kotesovec, Oct 23 2017: (Start)
a(n) = (3*n^2 + 3*n + 1)*a(n-1) - 3*n^4*a(n-2) + (n-1)^3*n^3*a(n-3).
a(n) ~ Pi * log(n)^2 * n^(2*n + 3) * (1 + 2*gamma/log(n) + (gamma^2 + Pi^2/6) / log(n)^2) / exp(2*n), where gamma is the Euler-Mascheroni constant (A001620). (End)
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MATHEMATICA
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T[n_, k_] := If[k <= n, (n-k+2)!^k*Sum[(-1)^(j+1)*Binomial[n-k+2, j]/j^k, {j, 1, n-k+2}], 0]; a[n_] := T[n+1, 2]; Table[a[n], {n, 1, 10}] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A008969 *)
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CROSSREFS
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Essentially the same as A060237.
Column 2 in triangle A008969.
Sequence in context: A293055 A121020 A060237 * A207214 A000686 A102923
Adjacent sequences: A000421 A000422 A000423 * A000425 A000426 A000427
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Vaclav Kotesovec, Oct 23 2017
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STATUS
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approved
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