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Search: id:A128080
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| A128080 |
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Triangle, read by rows of n(n-1)+1 terms, of coefficients of q in the q-analog of the odd double factorials: T(n,k) = [q^k] Product_{j=1..n} (1-q^(2j-1))/(1-q) for n>0, with T(0,0)=1. |
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+0
11
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| 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 2, 1, 1, 3, 6, 9, 12, 14, 15, 14, 12, 9, 6, 3, 1, 1, 4, 10, 19, 31, 45, 60, 74, 86, 94, 97, 94, 86, 74, 60, 45, 31, 19, 10, 4, 1, 1, 5, 15, 34, 65, 110, 170, 244, 330, 424, 521, 614, 696, 760, 801, 815, 801, 760, 696, 614, 521, 424, 330, 244, 170
(list; table; graph; listen)
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OFFSET
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0,7
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LINKS
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Eric Weisstein's World of Mathematics, q-Factorial from MathWorld.
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EXAMPLE
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The row sums form A001147, the odd double factorial numbers:
[1,1,3,15,105,945,10395,135135, ..., (2n-1)!!, ...].
Triangle begins:
1;
1;
1,1,1;
1,2,3,3,3,2,1;
1,3,6,9,12,14,15,14,12,9,6,3,1;
1,4,10,19,31,45,60,74,86,94,97,94,86,74,60,45,31,19,10,4,1;
1,5,15,34,65,110,170,244,330,424,521,614,696,760,801,815,801,760,696,614,521,424,330,244,170,110,65,34,15,5,1;
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PROGRAM
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(PARI) {T(n, k)=if(k<0|k>n*(n-1), 0, if(n==0, 1, polcoeff(prod(j=1, n, (1-q^(2*j-1))/(1-q)), k, q)))}
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CROSSREFS
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Cf. A001147 ((2n-1)!!); A128081 (central terms), A128082 (diagonal), A128083 (row squared sums).
Sequence in context: A140733 A143605 A098418 this_sequence A062187 A031283 A096520
Adjacent sequences: A128077 A128078 A128079 this_sequence A128081 A128082 A128083
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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), Feb 14 2007
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