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A001247
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Squares of Bell numbers.
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20
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1, 1, 4, 25, 225, 2704, 41209, 769129, 17139600, 447195609, 13450200625, 460457244900, 17754399678409, 764214897046969, 36442551140059684, 1912574337188517025, 109833379421325769609, 6866586647633870998416, 465228769500062060333281
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OFFSET
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0,3
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REFERENCES
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C. M. Bender, D. C. Brody and B. K. Meister, Quantum Field Theory of Partitions, J. Math. Phys., 40,7 (1999), 3239-45.
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LINKS
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FORMULA
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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).
E.g.f.: exp(-2)*Sum(exp(exp(n*x))/n!, n = 0..infinity). - Vladeta Jovovic, Jan 31 2008
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MAPLE
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MATHEMATICA
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PROG
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(Sage) [(bell_number(n))^2 for n in range(0, 18)] # Zerinvary Lajos, May 15 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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