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MAPLE
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restart; nmax:=13; jn:=nmax+1: im:=nmax+1: 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)!); LAMBDA(-2, n):= sum(2*(1-2^(2*k-1))*(-bernoulli(2*k)/ (2*k))*(-1)^(k+n)* cfn2(n+1-k, n), k=1..n)/ factorial(2*n-2) end do: Lcgz(2):=1/12: f(2):=1/12: for n from 3 to nmax do Lcgz(n):=LAMBDA(-2, n-1)/((2*n-2)*(2*n-3)): f(n):= Lcgz(n)-((2*n-3)/(2*n-2))*f(n-1) end do: for n from 1 to nmax do b(n):=denom(Lcgz(n+1)) end do: for n from 1 to nmax do b(n):=2*n*denom(Delta(n-1))/2^(2*n) end do: p(2):=b(1): for n from 2 to nmax do p(n+1):= lcm(p(n)*(2*n)*(2*n-1), b(n)) end do: for n from 2 to nmax do LAMBDA(n, 1) :=p(n)*f(n) end do: a:=n->LAMBDA(n, 1): seq(a(n), n=2..nmax);
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