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A014070 a(n) = binomial(2^n, n).

%I A014070 #40 Feb 15 2023 13:32:13
%S A014070 1,2,6,56,1820,201376,74974368,94525795200,409663695276000,
%T A014070 6208116950265950720,334265867498622145619456,
%U A014070 64832175068736596027448301568,45811862025512780638750907861652480,119028707533461499951701664512286557511680
%N A014070 a(n) = binomial(2^n, n).
%C A014070 a(n) is the number of n X n (0,1) matrices with distinct rows modulo rows permutations. - Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 13 2003
%H A014070 Vincenzo Librandi, <a href="/A014070/b014070.txt">Table of n, a(n) for n = 0..60</a>
%F A014070 G.f.: A(x) = Sum_{n>=0} log(1 + 2^n*x)^n / n!. - _Paul D. Hanna_, Dec 28 2007
%F A014070 a(n) = (1/n!) * Sum_{k=0..n} Stirling1(n, k) * 2^(n*k). - _Paul D. Hanna_, Feb 05 2023
%F A014070 From _Vaclav Kotesovec_, Jul 02 2016: (Start)
%F A014070 a(n) ~ 2^(n^2) / n!.
%F A014070 a(n) ~ 2^(n^2 - 1/2) * exp(n) / (sqrt(Pi) * n^(n+1/2)).
%F A014070 (End)
%p A014070 A014070:= n-> binomial(2^n,n); seq(A014070(n), n=0..20); # _G. C. Greubel_, Mar 14 2021
%t A014070 Table[Binomial[2^n,n],{n,0,20}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 03 2011 *)
%o A014070 (PARI) a(n)=binomial(2^n,n)
%o A014070 (PARI) /* G.f. A(x) as Sum of Series: */
%o A014070 a(n)=polcoeff(sum(k=0,n,log(1+2^k*x +x*O(x^n))^k/k!),n) \\ _Paul D. Hanna_, Dec 28 2007
%o A014070 (PARI) {a(n) = (1/n!) * sum(k=0,n, stirling(n, k, 1) * 2^(n*k) )}
%o A014070 for(n=0,20,print1(a(n),", ")) \\ _Paul D. Hanna_, Feb 05 2023
%o A014070 (Magma) [Binomial(2^n, n): n in [0..25]]; // _Vincenzo Librandi_, Sep 13 2016
%o A014070 (Sage) [binomial(2^n, n) for n in (0..20)] # _G. C. Greubel_, Mar 14 2021
%Y A014070 Sequences of the form binomial(2^n +p*n +q, n): A136556 (0,-1), this sequence (0,0), A136505 (0,1), A136506 (0,2), A060690 (1,-1), A132683 (1,0), A132684 (1,1), A132685 (2,0), A132686 (2,1), A132687 (3,-1), A132688 (3,0), A132689 (3,1).
%Y A014070 Cf. A088229, A136393, A136555.
%K A014070 nonn,easy
%O A014070 0,2
%A A014070 _N. J. A. Sloane_