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%I #12 Feb 04 2019 05:57:51
%S 1,1,1,2,2,2,5,8,8,5,17,39,61,39,17,79,287,556,556,287,79,554,2792,
%T 6910,9058,6910,2792,554,5283,34650,103212,171195,171195,103212,34650,
%U 5283,65346,510593,1783325,3559031,4449494,3559031,1783325,510593,65346
%N Triangle read by rows: The number of chord diagrams on 2n vertices with m marked chords.
%H Andrew Howroyd, <a href="/A322176/b322176.txt">Table of n, a(n) for n = 0..1274</a>
%H R. J. Mathar, <a href="/A322176/a322176.pdf">Marked Chord Diagrams A322176</a>
%H R. J. Mathar, <a href="http://vixra.org/abs/1901.0148">Feynman diagrams of the QED vacuum polarization</a>, vixra:1901.0148 (2019)
%F T(n,m) = T(n,n-m).
%F T(n,0) = A054499(n).
%e 1;
%e 1, 1;
%e 2, 2, 2;
%e 5, 8, 8, 5;
%e 17, 39, 61, 39, 17;
%e 79, 287, 556, 556, 287, 79;
%o (PARI)
%o C(p, d)={sum(k=0, p\2, binomial(p, 2*k) * (d*(1+y^d))^k * if(d%2, p==2*k, (1+y^(d/2))^(p-2*k)) * (2*k)!/(2^k*k!))}
%o R(n)={sum(k=0, n\2, binomial(n,2*k) * (1+y^2)^k * (1+y)^(n-2*k) * (2*k)!/k!)}
%o row(n)={Vec(if(n==0, 1, (sumdiv(2*n, d, eulerphi(d)*C(2*n/d, d))/n + R(n) + (1+y)*R(n-1))/4))}
%o { for(n=0, 8, print(row(n))) } \\ _Andrew Howroyd_, Dec 13 2018
%Y Cf. A054499.
%K nonn,tabl
%O 0,4
%A _R. J. Mathar_, Nov 30 2018
%E Terms a(21) and beyond from _Andrew Howroyd_, Dec 13 2018
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