A051545 Second unsigned column of triangle A051339.

0, 1, 15, 191, 2414, 31594, 434568, 6314664, 97053936, 1576890000, 27046454400, 488849155200, 9293295110400, 185464792800000, 3878247384345600, 84822225638169600, 1937048605944883200, 46113230058645657600

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

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

References

• Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051339.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..440

Crossrefs

Cf. A001730 (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..(this sequence), k=7..A051560, k=8..A051562, k=9..A051564. - Gary Detlefs, Jan 04 2011

Programs

Mathematica

f[k_] := k + 6; 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 *)

Formula

a(n) = A051339(n, 2)*(-1)^(n-1).

E.g.f.: -log(1-x)/(1-x)^7.

a(n) = n!*Sum_{k=0,..,n-1}((-1)^k*binomial(-7,k)/(n-k)), for n>=1. - Milan Janjic, Dec 14 2008

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