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A001722
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Generalized Stirling numbers.
(Formerly M5061 N2191)
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2
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1, 18, 251, 3325, 44524, 617624, 8969148, 136954044, 2201931576, 37272482280, 663644774880, 12413008539360, 243533741849280, 5003753991174720, 107497490419296000, 2410964056571616000, 56366432074677312000, 1371711629236971456000, 34699437370290760704000
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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=3,n=5) ~ exp(-x)/x^3*(1 - 18/x + 251/x^2 - 3325/x^3 + 44524/x^4 - 617624/x^5 + ... ) leads to the sequence given above. See A163931 and A163932 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+2, 2)*5^k*Stirling1(n+2, k+2). - 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-2) = |f(n,2,5)|, for n >= 2. - Milan Janjic, Dec 21 2008
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MATHEMATICA
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Table[Sum[(-1)^(n + k)*Binomial[k + 2, 2]*5^k*StirlingS1[n + 2, k + 2], {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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