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 A051564 Second unsigned column of triangle A051523. 17
 0, 1, 21, 362, 6026, 101524, 1763100, 31813200, 598482000, 11752855200, 240947474400, 5154170774400, 114942011990400, 2669517204076800, 64496340380102400, 1619153396908185600, 42188624389562112000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS From Johannes W. Meijer, Oct 20 2009: (Start) The asymptotic expansion of the higher order exponential integral E(x,m=2,n=10) ~ exp(-x)/x^2*(1 - 21/x + 362/x^2 - 6026/x^3 + 101524/x^4 - 1763100/x^5 + 31813200/x^6 - ...) leads to the sequence given above. See A163931 and A028421 for more information. (End) REFERENCES Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051523. LINKS G. C. Greubel, Table of n, a(n) for n = 0..440 FORMULA a(n) = A051523(n, 2)*(-1)^(n-1). E.g.f.: -log(1-x)/(1-x)^10. a(n) = n!*Sum_{k=0..n-1}((-1)^k*binomial(-10,k)/(n-k)), for n>=1. - Milan Janjic, Dec 14 2008 a(n) = n!*[9]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 MATHEMATICA f[n_] := n!*Sum[(-1)^k*Binomial[-10, k]/(n - k), {k, 0, n - 1}]; Array[f, 17, 0] Range[0, 16]! CoefficientList[ Series[-Log[(1 - x)]/(1 - x)^10, {x, 0, 16}], x] (* Or, using elementary symmetric functions: *) f[k_] := k + 9; t[n_] := Table[f[k], {k, 1, n}] a[n_] := SymmetricPolynomial[n - 1, t[n]] Table[a[n], {n, 1, 16}] (* Clark Kimberling, Dec 29 2011 *) CROSSREFS Cf. A049398 (first unsigned column). Related to n!*the k-th successive summation of the harmonic numbers: k=0..A000254, k=1..A001705, k=2..A001711, k=3..A001716, k=4..A001721, k=5..A051524, k=6..A051545, k=7..A051560, k=8..A051562, k=9..A051564. - Gary Detlefs Jan 04 2011 Sequence in context: A192093 A006105 A167032 * A302308 A303039 A302876 Adjacent sequences:  A051561 A051562 A051563 * A051565 A051566 A051567 KEYWORD easy,nonn AUTHOR STATUS approved

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Last modified February 19 13:17 EST 2020. Contains 332044 sequences. (Running on oeis4.)