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A001723
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Generalized Stirling numbers.
(Formerly M5189 N2256)
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3
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1, 26, 485, 8175, 134449, 2231012, 37972304, 668566300, 12230426076, 232959299496, 4623952866312, 95644160132976, 2060772784375824, 46219209678691200, 1078100893671811200, 26129183717351462400, 657337657573760947200, 17147815411007234188800
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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=4,n=5) ~ exp(-x)/x^4*(1 - 26/x + 485/x^2 - 8175/x^3 + 134449/x^4 - 2231012/x^5 + ...) leads to the sequence given above. See A163931 and A163934 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(3+k, 3)*5^k*Stirling1(n+3, k+3). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j), then a(n-3) = |f(n,3,5)|, for n >= 3. - Milan Janjic, Dec 21 2008
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MATHEMATICA
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Table[Sum[(-1)^(n + k)*Binomial[k + 3, 3]*5^k*StirlingS1[n + 3, k + 3], {k, 0, n}], {n, 0, 20}] (* T. D. Noe, Aug 10 2012 *)
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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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