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 A051562 Second unsigned column of triangle A051380. 17
 0, 1, 19, 299, 4578, 71394, 1153956, 19471500, 343976400, 6366517200, 123418922400, 2503748556000, 53091962697600, 1175271048201600, 27123099523027200, 651708291206649600, 16282170039031142400 (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=9) ~ exp(-x)/x^2*(1 - 19/x + 299/x^2 - 4578/x^3 + 71394/x^4 - 1153956/x^5 + 19471500/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 A051380. LINKS G. C. Greubel, Table of n, a(n) for n = 0..440 FORMULA a(n) = A051380(n, 2)*(-1)^(n-1). E.g.f.: -log(1-x)/(1-x)^9. a(n) = n!*Sum_{k=0..n-1} ((-1)^k*binomial(-9,k)/(n-k)), for n>=1. - Milan Janjic, Dec 14 2008 a(n) = n!*[8]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[k_] := k + 8; 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. A049389 (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: A155017 A199245 A152591 * A324359 A074460 A267010 Adjacent sequences:  A051559 A051560 A051561 * A051563 A051564 A051565 KEYWORD easy,nonn AUTHOR STATUS approved

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Last modified December 5 23:39 EST 2019. Contains 329784 sequences. (Running on oeis4.)