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A051545 Second unsigned column of triangle A051339. 17
0, 1, 15, 191, 2414, 31594, 434568, 6314664, 97053936, 1576890000, 27046454400, 488849155200, 9293295110400, 185464792800000, 3878247384345600, 84822225638169600, 1937048605944883200, 46113230058645657600 (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=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.

(End)

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

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

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 *)

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

Sequence in context: A145601 A004344 A038339 * A220528 A006238 A201883

Adjacent sequences:  A051542 A051543 A051544 * A051546 A051547 A051548

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified December 9 03:27 EST 2019. Contains 329872 sequences. (Running on oeis4.)