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Search: id:A000464
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| A000464 |
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Expansion of sin x /cos 2x.
(Formerly M4812 N2059)
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+0
5
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| 1, 11, 361, 24611, 2873041, 512343611, 129570724921, 44110959165011, 19450718635716001, 10784052561125704811, 7342627959965776406281, 6023130568334172003579011, 5858598896811701995459355761
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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D. Dumont, Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers, Adv. Appl. Math., 16 (1995), 275-296.
J. W. L. Glaisher, "On the coefficients in the expansions of cos x/ cos 2x and sin x/ cos 2x", Quart. J. Pure and Applied Math., 45 (1914), 187-222.
I. J. Schwatt, Intro. to Operations with Series, Chelsea, p. 278.
D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..50
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FORMULA
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E.g.f.: Sum_{k>=0} a(k)x^(2k+1)/(2k+1)! = sin(x)/cos(2x).
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PROGRAM
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(PARI) a(n)=if(n<0, 0, n+=n+1; n!*polcoeff(sin(x+x*O(x^n))/cos(2*x+x*O(x^n)), n)) /* Michael Somos Feb 09 2006 */
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CROSSREFS
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Cf. A064073. Bisection of A000822, A001586.
Sequence in context: A012138 A067428 A066268 this_sequence A024149 A018893 A051862
Adjacent sequences: A000461 A000462 A000463 this_sequence A000465 A000466 A000467
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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Better description, new reference 8/95.
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