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%I #7 Sep 20 2012 13:58:14
%S 9,450,99225,3572100,1080560250,547844046750,28761812454375,
%T 66497310394515000,324074642207668852500,170139187159026147562500,
%U 495019965039186576333093750,74252994755877986449964062500
%N The p(n) sequence that is associated with the Zeta triangle A160474
%F a(n) = 3*2^(3-2*n)*(2*n-1)!*A160476(n), for n = 2, 3, .. , with A160476 the first right hand column of the Zeta triangle.
%p nmax:=15: with(combinat): cfn1 := proc(n, k): sum((-1)^j*stirling1(n+1, n+1-k+j) * stirling1(n+1, n+1-k-j), j=-k..k) end proc: Omega(0) := 1: for n from 1 to nmax do Omega(n) := (sum((-1)^(k1+n+1)*(bernoulli(2*k1)/(2*k1))*cfn1(n-1, n-k1), k1=1..n))/(2*n-1)! end do: for n from 1 to nmax do d(n) := 2^(2*n-1)*Omega(n) end do: for n from 2 to nmax do Zc(n-1) := d(n-1)*2/((2*n-1)*(n-1)) end do: c(1) := denom(Zc(1)): for n from 1 to nmax-1 do c(n+1) := lcm(c(n)*(n+1)*(2*n+3)/2, denom(Zc(n+1))): p(n+1) := c(n) end do: seq(p(n), n=2..nmax);
%p # (program edited, _Johannes W. Meijer_, Sep 20 2012)
%Y Cf. A160474 and A160476.
%K easy,nonn
%O 2,1
%A _Johannes W. Meijer_, May 24 2009
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