A091546 - OEIS

%I #7 Oct 12 2012 14:40:20

%S 1,56,10192,3872960,2517424000,2497284608000,3511182158848000,

%T 6643156644540416000,16275733779124019200000,

%U 50129260039701979136000000,189588861470152885092352000000,863766852858016544480755712000000

%N First column of the array A092077 ((8,2)-Stirling2).

%C Also seventh column (m=6) of triangle A091543.

%D P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.

%F a(n)= (2^(n-1))*product((3*j+1)*(6*j+1), j=0..n-1), n>=1. From eq.12 of the Blasiak et al. reference with r=8, s=2, k=1.

%F a(n)= (6^(2*n))*risefac(1/6, n)*risefac(1/3, n)/2, n>=1, with risefac(x, n) = Pochhammer(x, n).

%F a(n)= fac6(6*n-5)*fac6(6*n-4)/2, n>=1, with fac6(6*n-5) = A008542(n) and fac6(6*n-4)/2 = A034689(n)= (2^(n-1))*A007559(n), (6-factorials).

%K nonn,easy

%O 1,2

%A _Wolfdieter Lang_, Feb 13 2004