Search: id:A001193
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%I A001193 M1944 N0770
%S A001193 1,2,9,60,525,5670,72765,1081080,18243225,344594250,7202019825,
%T A001193 164991726900,4111043861925,110681950128750,3201870700153125,
%U A001193 99044533658070000,3262279327362680625,113987877673731311250
%N A001193 (n+1)(2n)!/(2^n*n!) (or (n+1)(2n-1)!!).
%C A001193 Solution to y'=A(x), y(0)=0 satisfies 0=x^2+2*y^2*x-y^2. - Michael Somos 
               Mar 11 2004
%D A001193 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001193 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001193 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 167.
%F A001193 E.g.f.: (1-x)/(1-2x)^(3/2) = d/dx x/(1-2x)^(1/2).
%p A001193 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]
%o A001193 (PARI) a(n)=if(n<0,0,(n+1)*(2*n)!/(2^n*n!))
%Y A001193 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 12 
               2009: (Start)
%Y A001193 Equals the first right hand column of A167591.
%Y A001193 Equals the first left hand column of A167594.
%Y A001193 (End)
%Y A001193 Sequence in context: A116364 A120970 A111558 this_sequence A161391 A120014 
               A036774
%Y A001193 Adjacent sequences: A001190 A001191 A001192 this_sequence A001194 A001195 
               A001196
%K A001193 nonn,easy
%O A001193 0,2
%A A001193 N. J. A. Sloane (njas(AT)research.att.com).
%E A001193 Better description from Wouter Meeussen (wouter.meeussen(AT)pandora.be), 
               Mar 08 2001
%E A001193 More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 01 2000

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