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

0,5

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

Table of n, a(n) for n=0..92.

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