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A001708
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Generalized Stirling numbers.
(Formerly M5095 N2206)
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3
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1, 20, 295, 4025, 54649, 761166, 11028590, 167310220, 2664929476, 44601786944, 784146622896, 14469012689040, 279870212258064, 5667093514231200, 119958395537083104, 2650594302549806976, 61049697873641191296, 1463708634867162093312, 36482312832434713195776
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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=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. - 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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E.g.f.: ( log ( 1 - x ))^4 / 24 ( 1 - x )^2.
a(n) = Sum_{k=0..n} (-1)^(n+k)*binomial(k+4, 4)*2^k*Stirling1(n+4, k+4). - 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-4) = |f(n,4,2)| for n >= 4. - Milan Janjic, Dec 21 2008
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MATHEMATICA
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With[{nn=20}, Drop[CoefficientList[Series[Log[1-x]^4/(24(1-x)^2), {x, 0, nn}], x]Range[0, nn]!, 4]] (* Harvey P. Dale, Oct 24 2011 *)
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PROG
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(PARI) my(x='x+O('x^25)); Vec(serlaplace((log(1-x))^4/(24*(1-x)^2))) \\ Michel Marcus, Feb 04 2022
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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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