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Search: id:A128596
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| A128596 |
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Triangle, read by rows, of coefficients of q^(nk) in the q-analog of the even double factorials: T(n,k) = [q^(nk)] Product_{j=1..n} (1-q^(2j))/(1-q) for n>0, with T(0,0)=1. |
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+0
4
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| 1, 1, 1, 1, 2, 1, 1, 7, 7, 1, 1, 24, 46, 24, 1, 1, 86, 297, 297, 86, 1, 1, 315, 1919, 3210, 1919, 315, 1, 1, 1170, 12399, 32510, 32510, 12399, 1170, 1, 1, 4389, 80241, 318171, 484636, 318171, 80241, 4389, 1, 1, 16588, 520399, 3054100, 6730832, 6730832
(list; table; graph; listen)
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OFFSET
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0,5
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FORMULA
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T(n,k) = A128084(n,nk) where A128084 is the triangle of coefficients of q in the q-analog of the even double factorials.
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EXAMPLE
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Row sums equal 2*A000165(n-1) for n>0, twice the even double factorials:
[1, 2, 4, 16, 96, 768, 7680, 92160, 1290240, ..., 2*(2n-2)!!, ...].
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 7, 7, 1;
1, 24, 46, 24, 1;
1, 86, 297, 297, 86, 1;
1, 315, 1919, 3210, 1919, 315, 1;
1, 1170, 12399, 32510, 32510, 12399, 1170, 1;
1, 4389, 80241, 318171, 484636, 318171, 80241, 4389, 1;
1, 16588, 520399, 3054100, 6730832, 6730832, 3054100, 520399, 16588, 1;
1, 63064, 3382588, 28980565, 89514691, 127707302, 89514691, 28980565, 3382588, 63064, 1;
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PROGRAM
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(PARI) {T(n, k)=if(k<0|k>n^2, 0, if(n==0, 1, polcoeff(prod(j=1, n, (1-q^(2*j))/(1-q)), n*k, q)))}
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CROSSREFS
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Cf. A128084; A000165 ((2n)!!); A128086 (column 1), A128597 (column 2), A128598 (column 3); variant: A128592.
Sequence in context: A039760 A122021 A015110 this_sequence A139349 A120475 A086738
Adjacent sequences: A128593 A128594 A128595 this_sequence A128597 A128598 A128599
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 12 2007
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