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%I #21 May 08 2020 18:25:27
%S 1,2,8,45,315,2634,25518,280257,3434595,46400310,684374076,
%T 10933866027,187983528813,3458845917990,67787903801790,
%U 1409293876400019,30968525550983913,717023025711440082,17442766619178969600,444704318660973471885,11855331996299677291131
%N Number of n X n symmetric binary matrices with no row sum greater than 2.
%H Nathaniel Johnston, <a href="/A139678/b139678.txt">Table of n, a(n) for n = 0..200</a>
%H Art of Problem Solving forum, <a href="http://www.artofproblemsolving.com/Forum/viewtopic.php?t=402119">A recursive formula please</a>
%F E.g.f.: exp( (6x + x^2 + x^3)/(4(1 - x)) ) / sqrt(1 - x). - _Joel B. Lewis_, Apr 17 2011, corrected by _Vaclav Kotesovec_, Aug 13 2013
%F a(n) ~ n^n*exp(2*sqrt(2*n)-n-7/4)/sqrt(2) * (1+17/(6*sqrt(2*n))). - _Vaclav Kotesovec_, Aug 13 2013
%F Recurrence: 2*a(n) = 4*n*a(n-1) - 2*(n-2)*(n-1)*a(n-2) + (n-2)*(n-1)*a(n-3) - (n-3)*(n-2)*(n-1)*a(n-4). - _Vaclav Kotesovec_, Aug 13 2013
%p n:=18: G:=taylor((1/sqrt(1-x))*exp((6*x + x^2 + x^3)/(4 - 4*x)),x=0,n+1): seq(coeff(G,x,m)*m!,m=0..n); # _Nathaniel Johnston_, Apr 19 2011
%o (PARI) seq(n) ={Vec(serlaplace(exp( (6*x + x^2 + x^3)/(4*(1 - x)) + O(x*x^n) ) / sqrt(1 - x + O(x*x^n))))} \\ _Andrew Howroyd_, May 08 2020
%Y Column k=2 of A334548.
%K nonn
%O 0,2
%A _R. H. Hardin_, Jun 13 2008
%E a(19)-a(20) added from b-file by _Andrew Howroyd_, May 08 2020
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