A052249 Triangle T(n,k) (n >= 1, k >= 1) giving dimension of bigrading of Connes-Moscovici noncocommutative algebra.

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

Offset: 0

Author

David Broadhurst, Feb 05 2000

Keywords

• nonn
• tabl
• nice

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

Examples

			Triangle begins
  1;
  1, 1;
  0, 2, 1;
  0, 1, 3, 1;
  0, 0, 2, 4, 1;
  0, 0, 1, 4, 5, 1;
  ...
		

Links

• D. J. Broadhurst and D. Kreimer, Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees, arXiv:hep-th/0001202, 2000.

Crossrefs

Cf. A052250.

Programs

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 *)