Igor Pak has authored 2 sequences.
A307468
Cogrowth sequence for the Heisenberg group.
Original entry on oeis.org
1, 4, 28, 232, 2156, 21944, 240280, 2787320, 33820044, 424925872, 5486681368, 72398776344, 972270849512, 13247921422480, 182729003683352, 2546778437385032, 35816909974343308, 507700854900783784, 7246857513425470288, 104083322583897779656
Offset: 0
For n=1 the a(1)=4 words are x^{-1}x, xx^{-1}, y^{-1}y, yy^{-1}.
- Jay Pantone, Table of n, a(n) for n = 0..200
- Cédric Béguin, Alain Valette and Andrzej Zuk, On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper's operator, Journal of Geometry and Physics, 21 (1997), 337-356.
- D. Lind and K, Schmidt, A survey of algebraic actions of the discrete Heisenberg group, arXiv:1502.06243 [math.DS], 2015; Russian Mathematical Surveys, 70:4 (2015), 77-142.
Related cogrowth sequences: Z
A000984, Z^2
A002894, Z^3
A002896, (Z/kZ)^*2 for k = 2..5:
A126869,
A047098,
A107026,
A304979, Richard Thompson's group F
A246877. The cogrowth sequences for BS(N,N) for N = 2..10 are
A229644,
A229645,
A229646,
A229647,
A229648,
A229649,
A229650,
A229651,
A229652.
A014298
a(n) = 2^n * (3n)! / (2n+1)!.
Original entry on oeis.org
1, 2, 24, 576, 21120, 1048320, 65802240, 5000970240, 446557224960, 45830873088000, 5316381278208000, 687893507997696000, 98231192942070988800, 15345895252950201139200, 2603510504983275503616000, 476694375041453927694336000, 93692112621783944697741312000
Offset: 0
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List([0..20], n-> 2^n*Factorial(3*n)/Factorial(2*n+1) ); # G. C. Greubel, Jun 12 2019
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[2^n*Factorial(3*n)/Factorial(2*n+1): n in [0..20]]; // G. C. Greubel, Jun 12 2019
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Table[2^n (3n)!/(2n+1)!,{n,0,20}] (* Harvey P. Dale, Mar 19 2016 *)
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a(n) = 2^n * (3*n)! / (2*n+1)! \\ Michel Marcus, Jun 24 2013
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[2^n*factorial(3*n)/factorial(2*n+1) for n in (0..20)] # G. C. Greubel, Jun 12 2019
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