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%I #9 Sep 01 2016 10:24:19
%S 1,57,9367,3039037,1631142633,1306299636853,1458563053824871,
%T 2164056543968020185,4116264432907357578961,9762542731516508922640177,
%U 28237035023990471230544779095,97815632146487780258222172635029
%N Generalized Bell numbers B_{7,2}.
%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(A091747(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+5*(j-1), 2), j=1..n), k=2..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=7, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.
%t a[n_] := Sum[Product[FactorialPower[k+5*(j-1), 2], {j, 1, n}]/k!, {k, 2, Infinity}]/E; Array[a, 12] (* _Jean-François Alcover_, Sep 01 2016 *)
%Y Cf. A091748 (B_{6, 2}).
%K nonn,easy
%O 1,2
%A _Wolfdieter Lang_, Feb 27 2004