%I #15 Feb 16 2024 21:07:44
%S 0,0,0,0,1,1,21,2576,982926,898027452,1704360435624,6105200593277808,
%T 38418707658237401781,401351360962291322915332,
%U 6647604373581920953532817489,168016310022000683846928851914752,6273885184347679045743431356156590136
%N Number of labeled 5-arch graphs on n nodes.
%H Allan Bickle, <a href="https://digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article=1409&context=tag">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.
%H Saverio Caminiti and Emanuele G. Fusco, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL10/Caminiti/caminiti.html">On the Number of Labeled k-arch Graphs</a>, Journal of Integer Sequences, Vol 10 (2007), Article 07.7.5
%F The number of labeled 5-arch graphs with n>6 nodes is given by f(n,5,n-5-1,0,5) where f is the recursive function described by the PARI/GP code below.
%o (PARI) f(n,k,i,u,j)={ local(s=0); if (i==1, binomial(n-u,j)*binomial(u,k-j), for (c=0, min(k,n-(i-1)-(u+j)), s+=f(n,k,i-1,u+j,c) ); binomial(n-u,j)*binomial(u,k-j)*s ) }
%Y Cf. A098721-A098724, A131311-A131315.
%K nonn
%O 1,7
%A Saverio Caminiti and Emanuele G. Fusco (fusco(AT)di.uniroma1.it), Sep 18 2007
%E Edited by _N. J. A. Sloane_, Oct 02 2007
%E Terms a(11) and beyond from _Andrew Howroyd_, Nov 07 2019