Search: id:A100071
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%I A100071
%S A100071 0,1,2,6,12,30,60,140,280,630,1260,2772,5544,12012,24024,51480,102960,
%T A100071 218790,437580,923780,1847560,3879876,7759752,16224936,32449872,
%U A100071 67603900,135207800,280816200,561632400,1163381400,2326762800
%N A100071 An inverse Chebyshev transform of n.
%C A100071 sum{k=0..floor(n/2), binomial(n-k,k)(-1)^k*A100071(n-2k)}=1.
%C A100071 Hankel transform is (-1)^n*n*2^(n-1), A085750. This is the inverse binomial 
               transform of -n. - Paul Barry (pbarry(AT)wit.ie), Jan 11 2007
%C A100071 Corollary 3 of "An Identity Involving the Least Common Multiple of Binomial 
               Coefficients and its Application" mentions this sequence. [From Roger 
               L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 08 2009]
%D A100071 Bakir Farhi, An Identity Involving the Least Common Multiple of Binomial 
               Coefficients and its Application, American Mathematical Monthly, 
               Nov. 2009, page 838 [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), 
               Nov 08 2009]
%F A100071 G.f.: 2x(1-sqrt(1-4x^2))/(sqrt(1-4x^2)(sqrt(1-4x^2)+2x-1)^2); G.f.: (1/
               sqrt(1-4x^2))x*c(x^2)/(1-x*c(x^2))^2; a(n)=sum{k=0..floor(n/2), binomial(n, 
               k)*(n-2k)}.
%F A100071 a(n)=n*C(n-1,floor((n-1)/2)); a(n)=sum(C(n,k)*2^(n-k)*C(2k-2,k-1)(-1)^(k-1),
               k,0,n); - Paul Barry (pbarry(AT)wit.ie), Jan 11 2007
%F A100071 Starting (1, 2, 6, 12,...), = inverse binomial transform of A134757: 
               (1, 3, 11, 37, 123, 401,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Nov 08 2007
%F A100071 a(n) = a(n-1)*n/floor(n/2) for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jan 20 2008
%F A100071 G.f.: x/((1-2x)*sqrt(1-4x^2)); - Paul Barry (pbarry(AT)wit.ie), Apr 25 
               2008
%F A100071 a(n) = (floor(n/2) + ceiling(n/2) + 1)!/(floor(n/2)! * ceiling(n/2)!) 
               [From Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 
               04 2008]
%p A100071 seq(seq(binomial(2*j,j)*j*i/2, i=1..2),j=0..15); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 28 2007
%t A100071 Table[(Floor[n/2] + Ceiling[n/2] + 1)!/(Floor[n/2]!*Ceiling[n/2]!), {n, 
               1, 40}] [From Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Nov 04 2008]
%t A100071 Table[If[n == 0, 0, n*Binomial[n - 1, Floor[(n - 1)/2]]], {n, 0, 30}] 
               [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 08 2009]
%Y A100071 Cf. A134757.
%Y A100071 Sequence in context: A058215 A166456 A162214 this_sequence A129912 A161507 
               A032177
%Y A100071 Adjacent sequences: A100068 A100069 A100070 this_sequence A100072 A100073 
               A100074
%K A100071 easy,nonn,new
%O A100071 0,3
%A A100071 Paul Barry (pbarry(AT)wit.ie), Nov 02 2004

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