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A128567
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Matrix square of Parker's partition triangle (A047812) read by rows.
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3
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1, 2, 1, 5, 6, 1, 14, 31, 14, 1, 42, 133, 117, 22, 1, 132, 587, 813, 300, 36, 1, 429, 2531, 4871, 2896, 692, 52, 1, 1430, 10950, 27743, 23961, 9206, 1430, 76, 1, 4862, 47185, 151208, 175734, 96418, 24598, 2798, 104, 1, 16796, 203704, 804065, 1200301
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column 0 is the Catalan numbers (A000108). Parker's partition triangle may be defined as: A047812(n,k) = [q^(nk+2k)] in the central q-binomial coefficient [2n+2,n+1] for n>=k>=0.
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EXAMPLE
| Triangle begins:
1;
2, 1;
5, 6, 1;
14, 31, 14, 1;
42, 133, 117, 22, 1;
132, 587, 813, 300, 36, 1;
429, 2531, 4871, 2896, 692, 52, 1;
1430, 10950, 27743, 23961, 9206, 1430, 76, 1;
4862, 47185, 151208, 175734, 96418, 24598, 2798, 104, 1;
16796, 203704, 804065, 1200301, 882471, 329426, 62885, 5236, 146, 1;
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PROG
| (PARI) {T(n, k)=local(M); M=matrix(n+1, n+1, r, c, if(r<c, 0, if(r==0, 1, polcoeff(prod(j=r+1, 2*r, 1-q^j)/prod(j=1, r, 1-q^j), (r+1)*(c-1), q)))); (M^2)[n+1, k+1]}
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CROSSREFS
| Cf. A047812; A128568 (column 1), A128569 (column 2), A128602 (row sums).
Sequence in context: A047887 A120986 A095801 * A179455 A039810 A124575
Adjacent sequences: A128564 A128565 A128566 * A128568 A128569 A128570
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Mar 12 2007
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