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Search: id:A001193
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| A001193 |
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(n+1)(2n)!/(2^n*n!) (or (n+1)(2n-1)!!).
(Formerly M1944 N0770)
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+0
5
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| 1, 2, 9, 60, 525, 5670, 72765, 1081080, 18243225, 344594250, 7202019825, 164991726900, 4111043861925, 110681950128750, 3201870700153125, 99044533658070000, 3262279327362680625, 113987877673731311250
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Solution to y'=A(x), y(0)=0 satisfies 0=x^2+2*y^2*x-y^2. - Michael Somos Mar 11 2004
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 167.
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FORMULA
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E.g.f.: (1-x)/(1-2x)^(3/2) = d/dx x/(1-2x)^(1/2).
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MAPLE
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restart: G(x):=(1-x)/(1-2*x)^(3/2): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1], x) od:x:=0:seq(f[n], n=0..17); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2009]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, (n+1)*(2*n)!/(2^n*n!))
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CROSSREFS
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Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 12 2009: (Start)
Equals the first right hand column of A167591.
Equals the first left hand column of A167594.
(End)
Sequence in context: A120970 A111558 A168449 this_sequence A161391 A120014 A036774
Adjacent sequences: A001190 A001191 A001192 this_sequence A001194 A001195 A001196
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better description from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Mar 08 2001
More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 01 2000
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