A001247 Squares of Bell numbers.

1, 1, 4, 25, 225, 2704, 41209, 769129, 17139600, 447195609, 13450200625, 460457244900, 17754399678409, 764214897046969, 36442551140059684, 1912574337188517025, 109833379421325769609, 6866586647633870998416, 465228769500062060333281

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• C. M. Bender, D. C. Brody and B. K. Meister, Quantum Field Theory of Partitions, J. Math. Phys., 40,7 (1999), 3239-45.

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• C. M. Bender et al., Combinatorics and Field theory, arXiv:quant-ph/0604164, 2006.

Crossrefs

Cf. A000110.

Programs

Magma

[Bell(n)^2: n in [0..20]]; // Vincenzo Librandi, Jul 16 2013

Maple

with(combinat): seq(bell(n)^2), n=0..17); # Zerinvary Lajos, Sep 21 2007

Mathematica

Table[BellB[n, 1]^2, {n, 0, 17}] (* Zerinvary Lajos, Jul 16 2009 *)

Sage

[(bell_number(n))^2 for n in range(0, 18)] # Zerinvary Lajos, May 15 2009

Formula

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