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a(n) = floor( 2^(n*(n-1)/2) / n! ).
(Formerly M1870)
1

%I M1870 #15 Nov 03 2022 05:46:24

%S 1,1,1,2,8,45,416,6657,189372,9695869,902597327,154043277297,

%T 48535481831642,28400190511772276,31020581422991798557,

%U 63530150754287203445810,244912468225468597942626507,1783398168624923337196441201196,24605638395579573858211783276124626

%N a(n) = floor( 2^(n*(n-1)/2) / n! ).

%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 246.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H G. C. Greubel, <a href="/A003091/b003091.txt">Table of n, a(n) for n = 1..85</a>

%F a(n) = floor( 2^binomial(n,2) / n! ).

%p A003091:n->floor(2^(n*(n-1)/2)/n!);

%t Table[Floor[2^(n*(n-1)/2)/n!], {n,30}] (* _G. C. Greubel_, Nov 02 2022 *)

%o (Magma) [Floor(2^Binomial(n,2)/Factorial(n)): n in [1..30]]; // _G. C. Greubel_, Nov 02 2022

%o (SageMath) [(2^binomial(n,2)//factorial(n)) for n in range(1,30)] # _G. C. Greubel_, Nov 02 2022

%K nonn,easy

%O 1,4

%A _N. J. A. Sloane_