Search: id:A160479
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%I A160479
%S A160479 10,21,2,11,13,1,34,57,5,23,1,1,29,31,2,1,37,1,41,301,1,47,1,1,53,3,1,
%T A160479 59,61,1,2,67,1,71,73,1,1,79,1,83,1,1,89,1,1,1,97,1,505,103,1,107,109,
%U A160479 11,113,1,1,1,1,1,1,127,2,131
%N A160479 The ZL(n) sequence of the Zeta and Lambda triangles A160474 and A160487
%C A160479 The rather strange ZL(n) sequence rules both the Zeta and Lambda triangles.
%C A160479 The Zeta triangle led to the first and the Lambda triangle to the second 
               Maple algorithm.
%F A160479 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 07 
               2009: (Start)
%F A160479 a(n) = A160476(n)/A160476(n-1)
%F A160479 (End)
%p A160479 restart; nmax:=65; jn:=nmax: im:=nmax: Omega(0):=1: for n from 1 to nmax 
               do for j from 1 to jn do cfn1(1, j):=1 end do: for i from 2 to im 
               do cfn1(i, 1):=0 end do: for j from 2 to jn do for i from 2 to im 
               do cfn1(i,j):=cfn1(i-1,j-1)*(j-1)^2+cfn1(i,j-1) end do end do: Omega(n):= 
               (sum((-1)^(k+n+1)*(bernoulli(2*k)/(2*k))*cfn1(n-k+1, n), k=1..n))/
               (2*n-1)! end do: for n from 1 to nmax do b(n):= 4^(-n)*(2*n+1)*n*denom(Omega(n)) 
               end do: c(1):=b(1): for n from 1 to nmax-1 do c(n+1):=lcm(c(n)*(n+1)*(2*n+3)/
               2, b(n+1)) end do: for n from 1 to nmax do cm(n):= c(n)*(1/6)* 4^n/
               (2*n+1)! end do: for n from 3 to nmax+1 do ZL(n):=cm(n-1)/cm(n-2) 
               end do: a:=n-> ZL(n): seq(a(n), n=3..nmax+1);
%p A160479 restart; nmax:=65; jn:=nmax: im:=nmax: for n from 1 to nmax do for i 
               from 2 to im do cfn2(i, 1):=0 end do: for j from 1 to jn do cfn2(1, 
               j):=1 end do: for j from 2 to jn do for i from 2 to im do cfn2(i,
               j):= cfn2(i, j-1) + cfn2(i-1, j-1)*(2*j-3)^2 end do end do: Delta(n-1):=sum((1-2^(2*k-1))* 
               (-1)^(n+1)*(-bernoulli(2*k)/(2*k))*(-1)^(k+n)*cfn2(n-k+1, n), k=1..n) 
               /(2*4^(n-1)*(2*n-1)!) end do: for n from 1 to nmax do b(n):= (2*n)*(2*n-1)*denom(Delta(n-1))/ 
               (2^(2*n)*(2*n-1)) end do: c(1):=b(1): for n from 1 to nmax-1 do c(n+1):=lcm(c(n)*(2*n+2)* 
               (2*n+1),b(n+1)) end do: for n from 1 to nmax do cm(n):= c(n)/(6*(2*n)!) 
               end do: for n from 3 to nmax+1 do ZL(n):=cm(n-1)/cm(n-2) end do: 
               a:=n-> ZL(n): seq(a(n), n=3..nmax+1);
%Y A160479 Cf. A160474 and A160487.
%Y A160479 The cnf1[m, n] are the central factorial numbers A008955.
%Y A160479 The cnf2[m, n] are the central factorial numbers A008956.
%Y A160479 Sequence in context: A006993 A038693 A018990 this_sequence A085222 A085221 
               A128536
%Y A160479 Adjacent sequences: A160476 A160477 A160478 this_sequence A160480 A160481 
               A160482
%K A160479 easy,nonn
%O A160479 3,1
%A A160479 Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009

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