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A001708
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Generalized Stirling numbers.
(Formerly M5095 N2206)
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1
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1, 20, 295, 4025, 54649, 761166, 11028590, 167310220, 2664929476, 44601786944, 784146622896, 14469012689040, 279870212258064, 5667093514231200, 119958395537083104, 2650594302549806976, 61049697873641191296
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 20 2009: (Start)
The asymptotic expansion of the higher order exponential integral E(x,m=5,n=2) ~ exp(-x)/x^5*(1 - 20/x + 295/x^2 - 4025/x^3 + 54649/x^4 - ...) leads to the sequence given above. See A163931 for E(x,m,n) information and A163932 for a Maple procedure for the asymptotic expansion.
(End)
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REFERENCES
| Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.
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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FORMULA
| E.g.f.: ( ln ( 1 - x ))^4 / 24 ( 1 - x )^2.
a(n)=sum((-1)^(n+k)*binomial(k+4, 4)*2^k*stirling1(n+4, k+4), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n-4) = |f(n,4,2)|, for n>=4. [From Milan R. Janjic (agnus(AT)blic.net), Dec 21 2008]
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MATHEMATICA
| With[{nn=20}, Drop[CoefficientList[Series[Log[1-x]^4/(24(1-x)^2), {x, 0, nn}], x]Range[0, nn]!, 4]] (* From Harvey P. Dale, Oct 24 2011 *)
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CROSSREFS
| Sequence in context: A047795 A132168 A069326 * A016255 A138794 A077758
Adjacent sequences: A001705 A001706 A001707 * A001709 A001710 A001711
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
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