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%I #8 Sep 01 2016 10:22:29
%S 1,73,15945,6993073,5124715761,5641397595321,8700819552421753,
%T 17898786381229403105,47345052327747786859873,
%U 156535091017683923932912041,632460052562874236182866885161
%N Generalized Bell numbers B_{8,2}.
%D P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
%D M. Schork, On the combinatorics of normal ordering bosonic operators and deforming it, J. Phys. A 36 (2003) 4651-4665.
%F a(n)=sum(A092077(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+6*(j-1), 2), j=1..n), k=2..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=8, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.
%t a[n_] := Sum[Product[FactorialPower[k+6*(j-1), 2], {j, 1, n}]/k!, {k, 2, Infinity}]/E; Array[a, 11] (* _Jean-François Alcover_, Sep 01 2016 *)
%Y Cf. A091749 (B_{7, 2}).
%K nonn,easy
%O 1,2
%A _Wolfdieter Lang_, Feb 27 2004
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