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A051562 Second unsigned column of triangle A051380. 17
0, 1, 19, 299, 4578, 71394, 1153956, 19471500, 343976400, 6366517200, 123418922400, 2503748556000, 53091962697600, 1175271048201600, 27123099523027200, 651708291206649600, 16282170039031142400 (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=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
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
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 *)
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
Sequence in context: A155017 A199245 A152591 * A330846 A324359 A074460
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)