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A051565
Third unsigned column of triangle A051523.
1
0, 0, 1, 33, 791, 17100, 358024, 7491484, 159168428, 3463513704, 77559615576, 1792139785920, 42789106278720, 1056302350122240, 26964471256888320, 711643650545422080, 19410244660543737600, 546854985563699289600
OFFSET
0,4
COMMENTS
From Johannes W. Meijer, Oct 20 2009: (Start)
The asymptotic expansion of the higher order exponential integral E(x,m=3,n=10) ~ exp(-x)/x^3*(1 - 33/x + 791/x^2 - 17100/x^3 + 358024/x^4 + ...) leads to the sequence given above. See A163931 and A163932 for more information.
(End)
REFERENCES
Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051523.
FORMULA
a(n) = A051523(n, 2)*(-1)^n; e.g.f.: ((log(1-x))^2)/(2*(1-x)^10).
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,2,10)|, for n>=1. - Milan Janjic, Dec 21 2008
CROSSREFS
Cf. A049398 (m=0), A051564 (m=1) unsigned columns.
Sequence in context: A021021 A164750 A100788 * A014931 A197358 A299074
KEYWORD
easy,nonn
STATUS
approved