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%I #19 Jul 02 2022 16:09:13
%S 1,2,6,44,716,24416,1680224,229468288,61820527104,32848197477760,
%T 34502874046006912,71850629135663531776,297429744309497638961920,
%U 2452504520881914016303901696,40340635076928240671195746599936,1324981038432182976845483456362661888,86953044949519288083916385603832568137728
%N Number of symmetric n X n (0,1)-matrices with pairwise distinct rows and columns.
%H G. C. Greubel, <a href="/A259763/b259763.txt">Table of n, a(n) for n = 0..80</a>
%H MathOverflow, <a href="http://mathoverflow.net/questions/210384/counting-matrices-of-special-types">Counting matrices of special types</a>, 2015.
%F a(n) = Sum_{k=0..n} Stirling1(n,k) * 2^(k*(k+1)/2).
%t Table[Sum[StirlingS1[n,k]*2^Binomial[k+1,2], {k,0,n}], {n,0,20}] (* _G. C. Greubel_, Nov 04 2018*)
%o (PARI) A259763(n) = sum(k=1,n, stirling(n,k,1) * 2^(k*(k+1)/2) );
%o (Magma) [(&+[StirlingFirst(n,k)*2^Binomial(k+1,2): k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Nov 04 2018
%Y Cf. A088310, A006024
%Y Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763
%K nonn
%O 0,2
%A _Max Alekseyev_, Jul 04 2015
%E a(0)=1 prepended by _Alois P. Heinz_, Jul 12 2015
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