A051562 Second unsigned column of triangle A051380.

0, 1, 19, 299, 4578, 71394, 1153956, 19471500, 343976400, 6366517200, 123418922400, 2503748556000, 53091962697600, 1175271048201600, 27123099523027200, 651708291206649600, 16282170039031142400

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

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. - Johannes W. Meijer, Oct 20 2009

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

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

Programs

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 *)

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