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A052249
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Triangle T(n,k) (n >= 1, k >= 1) giving dimension of bigrading of Connes-Moscovici noncocommutative algebra.
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0
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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; internal format)
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OFFSET
| 0,5
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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]
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LINKS
| D. J. Broadhurst and D. Kreimer, Towards cohomology of renormalization...
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EXAMPLE
| Triangle begins
1;
1,1;
0,2,1;
0,1,3,1;
0,0,2,4,1;
0,0,1,4,5,1; ...
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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} ] ] (* From Jean-François Alcover, Jan 23 2012, after David Callan *)
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CROSSREFS
| Cf. A052250.
Sequence in context: A195982 A129558 A131185 * A030528 A077227 A089263
Adjacent sequences: A052246 A052247 A052248 * A052250 A052251 A052252
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KEYWORD
| nonn,tabl,nice
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AUTHOR
| David Broadhurst (D.Broadhurst(AT)open.ac.uk), Feb 05 2000
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