This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A139678 #25 Apr 30 2025 23:16:22
%S A139678 1,2,8,45,315,2634,25518,280257,3434595,46400310,684374076,
%T A139678 10933866027,187983528813,3458845917990,67787903801790,
%U A139678 1409293876400019,30968525550983913,717023025711440082,17442766619178969600,444704318660973471885,11855331996299677291131
%N A139678 Number of n X n symmetric binary matrices with no row sum greater than 2.
%H A139678 Nathaniel Johnston, <a href="/A139678/b139678.txt">Table of n, a(n) for n = 0..200</a>
%H A139678 Art of Problem Solving forum, <a href="https://artofproblemsolving.com/community/c6h402119">A recursive formula please</a>
%F A139678 E.g.f.: exp( (6*x + x^2 + x^3)/(4*(1 - x)) ) / sqrt(1 - x). - _Joel B. Lewis_, Apr 17 2011, corrected by _Vaclav Kotesovec_, Aug 13 2013
%F A139678 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 A139678 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 A139678 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 A139678 (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 A139678 Column k=2 of A334548.
%K A139678 nonn
%O A139678 0,2
%A A139678 _R. H. Hardin_, Jun 13 2008
%E A139678 a(19)-a(20) added from b-file by _Andrew Howroyd_, May 08 2020