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A001721
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Generalized Stirling numbers.
(Formerly M4803 N2052)
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18
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1, 11, 107, 1066, 11274, 127860, 1557660, 20355120, 284574960, 4243508640, 67285058400, 1131047366400, 20099588140800, 376612896038400, 7422410595801600, 153516757766400000, 3325222830101760000, 75283691519393280000, 1778358268603445760000
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OFFSET
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0,2
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COMMENTS
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The asymptotic expansion of the higher order exponential integral E(x,m=2,n=5) ~ exp(-x)/x^2*(1 - 11/x + 107/x^2 - 1066/x^3 + 11274/x^4 - 127860/x^5 + 1557660/x^6 - ... ) leads to the sequence given above. See A163931 and A028421 for more information. - Johannes W. Meijer, Oct 20 2009
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REFERENCES
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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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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n+k)*binomial(k+1, 1)*5^k*Stirling1(n+1, k+1). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
a(n) = n!*Sum_{k=0..n-1} (-1)^k*binomial(-5,k)/(n-k). - Milan Janjic, Dec 14 2008
a(n) = n!*[4]h(n), where [k]h(n) denotes the k-th successive summation of the harmonic numbers from 0 to n. With offset 1. - Gary Detlefs, Jan 04 2011
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MATHEMATICA
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f[k_] := k + 4; t[n_] := Table[f[k], {k, 1, n}]; a[n_] := SymmetricPolynomial[n - 1, t[n]]; Table[a[n], {n, 1, 16}] (* Clark Kimberling, Dec 29 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
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STATUS
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approved
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