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

0,3

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.

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

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 *)

Prog

(Sage) [(bell_number(n))^2 for n in range(0, 18)] # Zerinvary Lajos, May 15 2009
(Magma) [Bell(n)^2: n in [0..20]]; // Vincenzo Librandi, Jul 16 2013

Crossrefs

Cf. A000110.

Sequence in context: A302587 A302608 A340337 * A031152 A010845 A087660

Adjacent sequences: A001244 A001245 A001246 * A001248 A001249 A001250

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved