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%I #17 Oct 07 2017 02:38:29
%S 1,1,1,0,2,1,0,1,3,1,0,0,2,4,1,0,0,1,4,5,1,0,0,0,2,6,6,1,0,0,0,1,4,9,
%T 7,1,0,0,0,0,2,7,12,8,1,0,0,0,0,1,4,11,16,9,1,0,0,0,0,0,2,7,16,20,10,
%U 1,0,0,0,0,0,1,4,12,23,25,11,1,0,0,0,0,0,0,2,7,18,31,30,12,1,0,0
%N Triangle T(n,k) (n >= 1, k >= 1) giving dimension of bigrading of Connes-Moscovici noncocommutative algebra.
%C With rows reversed, T(n,k) appears to be the number of partitions of n with k big parts, where a big part is a part >= 2 (0 <= k <= n/2). For example, with n=4, the 3 partitions 4, 31, 211 each have one big part. - _David Callan_, Aug 23 2011
%H D. J. Broadhurst and D. Kreimer, <a href="http://arXiv.org/abs/hep-th/0001202">Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees</a>, arXiv:hep-th/0001202, 2000.
%e Triangle begins
%e 1;
%e 1, 1;
%e 0, 2, 1;
%e 0, 1, 3, 1;
%e 0, 0, 2, 4, 1;
%e 0, 0, 1, 4, 5, 1;
%e ...
%t t[n_, k_] := Count[ IntegerPartitions[n], pp_ /; Count[pp, p_ /; p >= 2] == k]; Flatten[ Table[ t[n, k], {n, 1, 14}, {k, n-1, 0, -1} ] ] (* _Jean-François Alcover_, Jan 23 2012, after _David Callan_ *)
%Y Cf. A052250.
%K nonn,tabl,nice
%O 0,5
%A _David Broadhurst_, Feb 05 2000
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