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Search: id:A043301
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| A043301 |
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2^n*Sum_{ k=0..n } (n+k)!/((n-k)!*k!*4^k). |
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+0
7
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| 1, 3, 13, 77, 591, 5627, 64261, 857901, 13125559, 226566107, 4357258269, 92408688077, 2142828858847, 53940356223483, 1464960933469429, 42699628495507373, 1329548327094606279, 44045893308104036699
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Bruce Berndt, Ramanujan's Notebooks Part II, Springer-Verlag; see Integrals and Asymptotic Expansions, p. 229.
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and P roducts, 6th ed., Section 3.737.1, p. 423.
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FORMULA
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a(n)=(2*n-1)*a(n-1)+4*a(n-2), n>1.
2^(n+1)n!(e^2/Pi)*Integral(t=0, infinity, cos(2t)/(1+t^2)^(n+1)dt).
E.g.f.: 2*(e^2/Pi)*Integral(t=0, infinity, cos(2t)/(1+t^2-2x)dt).
2^n * y_n(1/2), where y_n(x) are the Bessel polynomials A001498.
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CROSSREFS
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Cf. A043302, A144505.
Sequence in context: A159662 A032035 A127127 this_sequence A141762 A062872 A159312
Adjacent sequences: A043298 A043299 A043300 this_sequence A043302 A043303 A043304
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KEYWORD
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nonn,easy
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 04 2002
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EXTENSIONS
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Edited by Michael Somos, Jul 16 2002
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