|
%I #34 Sep 08 2022 08:44:28
%S 1,1,4,25,225,2704,41209,769129,17139600,447195609,13450200625,
%T 460457244900,17754399678409,764214897046969,36442551140059684,
%U 1912574337188517025,109833379421325769609,6866586647633870998416,465228769500062060333281
%N Squares of Bell numbers.
%D C. M. Bender, D. C. Brody and B. K. Meister, Quantum Field Theory of Partitions, J. Math. Phys., 40,7 (1999), 3239-45.
%H T. D. Noe, <a href="/A001247/b001247.txt">Table of n, a(n) for n = 0..100</a>
%H C. M. Bender et al., <a href="http://arxiv.org/abs/quant-ph/0604164">Combinatorics and Field theory</a>, arXiv:quant-ph/0604164, 2006.
%F E.g.f.: exp(exp(x*(d_z) - 1))*(exp(exp(z) - 1)) |_{z = 0}, with the derivative operator d_z := d/dz. From equations (16) and (17) of Bender et al. (1999).
%F E.g.f.: exp(-2)*Sum(exp(exp(n*x))/n!, n = 0..infinity). - _Vladeta Jovovic_, Jan 31 2008
%p with(combinat): seq(bell(n)^2), n=0..17); # _Zerinvary Lajos_, Sep 21 2007
%t Table[BellB[n, 1]^2, {n, 0, 17}] (* _Zerinvary Lajos_, Jul 16 2009 *)
%o (Sage) [(bell_number(n))^2 for n in range(0, 18)] # _Zerinvary Lajos_, May 15 2009
%o (Magma) [Bell(n)^2: n in [0..20]]; // _Vincenzo Librandi_, Jul 16 2013
%Y Cf. A000110.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
|
