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A051524 Second unsigned column of triangle A051338. 17
0, 1, 13, 146, 1650, 19524, 245004, 3272688, 46536624, 703404576, 11277554400, 191338156800, 3427105248000, 64651956364800, 1281740285145600, 26648514872985600, 579892995734169600, 13183403757582643200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The asymptotic expansion of the higher order exponential integral E(x,m=2,n=6) ~ exp(-x)/x^2*(1 - 13/x + 146/x^2 - 1650/x^3 + 19524/x^4 - 245004/x^5 + 3272688/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 A051338.

LINKS

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

FORMULA

a(n) = A051338(n, 1)*(-1)^(n-1);

E.g.f.: -log(1-x)/(1-x)^6.

For n>=1, a(n) = n!*sum((-1)^k*binomial(-6,k)/(n-k),k=0..n-1). - Milan Janjic, Dec 14 2008

a(n) = n!*[5]h(n), where [k]h(n) denotes the k-th successive summation of h(n) from 0 to n. - Gary Detlefs Jan 04 2011

Conjecture: a(n) +(-2*n-9)*a(n-1) +(n+4)^2*a(n-2)=0. - R. J. Mathar, Aug 04 2013

MATHEMATICA

f[k_] := k + 5; 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. A001725 (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

Sequence in context: A152585 A014881 A048442 * A110748 A211072 A016135

Adjacent sequences:  A051521 A051522 A051523 * A051525 A051526 A051527

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified December 8 04:31 EST 2019. Contains 329850 sequences. (Running on oeis4.)