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A051561
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Third unsigned column of triangle A051379.
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1
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0, 0, 1, 27, 539, 9850, 176554, 3197348, 59354028, 1137868848, 22614500016, 466814750688, 10015620672672, 223359393479040, 5175622796192640, 124533006364442880, 3109120944743427840, 80473740053567016960
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 20 2009: (Start)
The asymptotic expansion of the higher order exponential integral E(x,m=3,n=8) ~ exp(-x)/x^3*(1 - 27/x + 539/x^2 - 9850/x^3 + 176554/x^4 + ...) leads to the sequence given above. See A163931 and A163932 for more information.
(End)
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REFERENCES
| Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051379.
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FORMULA
| a(n) = A051379(n, 2)*(-1)^n; e.g.f.: ((ln(1-x))^2)/(2*(1-x)^8).
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n) = |f(n,2,8)|, for n>=1. [From Milan R. Janjic (agnus(AT)blic.net), Dec 21 2008]
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CROSSREFS
| A049388 (m=0), A051560 (m=1) unsigned columns.
Sequence in context: A110896 A014928 A163199 * A163197 A061914 A076008
Adjacent sequences: A051558 A051559 A051560 * A051562 A051563 A051564
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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