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%I #13 Dec 23 2015 02:54:14
%S 1,4,36,372,4372,57396,828020,12962164,218098356,3915198836,
%T 74543140404,1497946963316,31640513815604,700059941981812,
%U 16175777760450868,389308305885650804,9736819496150623284,252548355023773152372
%N Number of B-diagrams G such that the number of vertices of G is |G|=n.
%C For a precise definition see the Bousbaa et al. link.
%H Imad Eddine Bousbaa, Ali Chouria, Jean-Gabriel Luque, <a href="http://arxiv.org/abs/1512.05937">A combinatorial Hopf algebra for the boson normal ordering problem</a>, arXiv:1512.05937 [math.CO], 2015.
%t T[0, 0] = 1; T[p_, q_] := T[p, q] = Sum[l! Binomial[j, l] Binomial[q - k + l, l] Binomial[i, j] Binomial[i, k] T[p - i, q - k + l], {i, 1, p}, {j, 0, i}, {k, 0, i}, {l, 0, j}]; a[n_] := Sum[T[n, q], {q, 0, n}]; Table[ a[n], {n, 0, 20}] (* _Jean-François Alcover_, Dec 21 2015 *)
%Y Cf. A265199.
%K nonn
%O 0,2
%A _Michel Marcus_, Dec 21 2015
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