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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

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-Fran├žois Alcover, Jan 23 2012, after David Callan *)

CROSSREFS

Cf. A052250.

Sequence in context: A131185 A286354 A296067 * 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 February 17 17:27 EST 2018. Contains 299296 sequences. (Running on oeis4.)