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Search: id:A003701
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| A003701 |
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Expansion of exp(x)/cos(x).
(Formerly M1259)
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+0
2
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| 1, 1, 2, 4, 12, 36, 152, 624, 3472, 18256, 126752, 814144, 6781632, 51475776, 500231552, 4381112064, 48656756992, 482962852096, 6034272215552, 66942218896384, 929327412759552, 11394877025289216, 174008703107274752
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of A000364 (with interpolated zeros). Hankel transform is A055209. [From Paul Barry (pbarry(AT)wit.ie), Jan 12 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.
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FORMULA
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G.f.: 1/(1-x-x^2/(1-x-4x^2/(1-x-9x^2/(1-x-16x^2.... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Jan 12 2009]
G.f.: exp(x)*sec(x) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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MAPLE
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restart: G(x):=exp(x)*sec(x): f[0]:=G(x): for n from 1 to 54 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..22 ); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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MATHEMATICA
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Exp[ x ]/Cos[ x ]
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CROSSREFS
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Cf. A062272, A062161.
Bisections are A000795 and A002084(n).
Sequence in context: A046993 A010551 A111942 this_sequence A114500 A148212 A149844
Adjacent sequences: A003698 A003699 A003700 this_sequence A003702 A003703 A003704
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
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Extended and reformatted 03/97.
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