Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #34 Jan 25 2023 13:29:31
%S 0,1,15,191,2414,31594,434568,6314664,97053936,1576890000,27046454400,
%T 488849155200,9293295110400,185464792800000,3878247384345600,
%U 84822225638169600,1937048605944883200,46113230058645657600
%N Second unsigned column of triangle A051339.
%C 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 Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051339.
%H G. C. Greubel, <a href="/A051545/b051545.txt">Table of n, a(n) for n = 0..440</a>
%F a(n) = A051339(n, 2)*(-1)^(n-1).
%F E.g.f.: -log(1-x)/(1-x)^7.
%F a(n) = n!*Sum_{k=0,..,n-1}((-1)^k*binomial(-7,k)/(n-k)), for n>=1. - _Milan Janjic_, Dec 14 2008
%F 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 f[k_] := k + 6; t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t Table[a[n], {n, 1, 16}]
%t (* _Clark Kimberling_, Dec 29 2011 *)
%Y Cf. A001730 (first unsigned column).
%Y 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 easy,nonn
%O 0,3
%A _Wolfdieter Lang_