A160478 The p(n) sequence that is associated with the Zeta triangle A160474.

9, 450, 99225, 3572100, 1080560250, 547844046750, 28761812454375, 66497310394515000, 324074642207668852500, 170139187159026147562500, 495019965039186576333093750, 74252994755877986449964062500

Offset: 2

Author

Johannes W. Meijer, May 24 2009

Keywords

• easy
• nonn

Crossrefs

Cf. A160474 and A160476.

Programs

Maple

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);
#  (program edited, Johannes W. Meijer, Sep 20 2012)

Formula

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.