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A051545 Second unsigned column of triangle A051339.

%I A051545 #34 Jan 25 2023 13:29:31
%S A051545 0,1,15,191,2414,31594,434568,6314664,97053936,1576890000,27046454400,
%T A051545 488849155200,9293295110400,185464792800000,3878247384345600,
%U A051545 84822225638169600,1937048605944883200,46113230058645657600
%N A051545 Second unsigned column of triangle A051339.
%C A051545 The asymptotic expansion of the higher order exponential integral E(x,m=2,n=7) ~ exp(-x)/x^2*(1 - 15/x + 191/x^2 - 2414/x^3 + 31594/x^4 - 434568/x^5 + 6314664/x^6 - ...) leads to the sequence given above. See A163931 and A028421 for more information. - _Johannes W. Meijer_, Oct 20 2009
%D A051545 Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051339.
%H A051545 G. C. Greubel, <a href="/A051545/b051545.txt">Table of n, a(n) for n = 0..440</a>
%F A051545 a(n) = A051339(n, 2)*(-1)^(n-1).
%F A051545 E.g.f.: -log(1-x)/(1-x)^7.
%F A051545 a(n) = n!*Sum_{k=0,..,n-1}((-1)^k*binomial(-7,k)/(n-k)), for n>=1. - _Milan Janjic_, Dec 14 2008
%F A051545 a(n) = n!*[6]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
%t A051545 f[k_] := k + 6; t[n_] := Table[f[k], {k, 1, n}]
%t A051545 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A051545 Table[a[n], {n, 1, 16}]
%t A051545 (* _Clark Kimberling_, Dec 29 2011 *)
%Y A051545 Cf. A001730 (first unsigned column).
%Y A051545 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..(this sequence), k=7..A051560, k=8..A051562, k=9..A051564. - _Gary Detlefs_, Jan 04 2011
%K A051545 easy,nonn
%O A051545 0,3
%A A051545 _Wolfdieter Lang_