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 A052249 Triangle T(n,k) (n >= 1, k >= 1) giving dimension of bigrading of Connes-Moscovici noncocommutative algebra. 0
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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 LINKS D. J. Broadhurst and D. Kreimer, Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees, arXiv:hep-th/0001202, 2000. EXAMPLE Triangle begins   1;   1, 1;   0, 2, 1;   0, 1, 3, 1;   0, 0, 2, 4, 1;   0, 0, 1, 4, 5, 1;   ... MATHEMATICA 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 *) CROSSREFS Cf. A052250. Sequence in context: A296067 A306713 A303810 * A030528 A077227 A089263 Adjacent sequences:  A052246 A052247 A052248 * A052250 A052251 A052252 KEYWORD nonn,tabl,nice AUTHOR David Broadhurst, Feb 05 2000 STATUS approved

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Last modified September 19 11:06 EDT 2019. Contains 327192 sequences. (Running on oeis4.)