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A051560
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Second unsigned column of triangle A051379.
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17
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0, 1, 17, 242, 3382, 48504, 725592, 11393808, 188204400, 3270729600, 59753750400, 1146140409600, 23046980025600, 485075533132800, 10669304848204800, 244861798361241600, 5854837379724748800
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OFFSET
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0,3
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COMMENTS
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The asymptotic expansion of the higher order exponential integral E(x,m=2,n=8) ~ exp(-x)/x^2*(1 - 17/x + 242/x^2 - 3382/x^3 + 48504/x^4 - 725592/x^5 + 11393808/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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Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051379.
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LINKS
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FORMULA
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E.g.f.: -log(1-x)/(1-x)^8.
a(n) = n!*Sum_{k=0..n-1} ((-1)^k*binomial(-8,k)/(n-k)), for n>=1. - Milan Janjic, Dec 14 2008
a(n) = n!*[7]h(n), where [k]h(n) denotes the k-th successive summation of the harmonic numbers from 0 to n. - Gary Detlefs, Jan 04 2011
Conjecture: a(n) +(-2*n-13)*a(n-1) +(n+6)^2*a(n-2)=0. - R. J. Mathar, Aug 04 2013
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MATHEMATICA
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f[k_] := k + 7; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}]
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CROSSREFS
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Cf. A049388 (first unsigned column).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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