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A160479
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The ZL(n) sequence of the Zeta and Lambda triangles A160474 and A160487
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5
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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, 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, 11, 113, 1, 1, 1, 1, 1, 1, 127, 2, 131
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| The rather strange ZL(n) sequence rules both the Zeta and Lambda triangles.
The Zeta triangle led to the first and the Lambda triangle to the second Maple algorithm.
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FORMULA
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 07 2009: (Start)
a(n) = A160476(n)/A160476(n-1)
(End)
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MAPLE
| 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);
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);
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CROSSREFS
| Cf. A160474 and A160487.
The cnf1[m, n] are the central factorial numbers A008955.
The cnf2[m, n] are the central factorial numbers A008956.
Sequence in context: A006993 A038693 A018990 * A085222 A085221 A128536
Adjacent sequences: A160476 A160477 A160478 * A160480 A160481 A160482
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KEYWORD
| easy,nonn
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AUTHOR
| Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009
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