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Search: id:A128592
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| A128592 |
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Triangle, read by rows, of coefficients of q^(nk+k) in the q-analog of the odd double factorials: T(n,k) = [q^(nk+k)] Product_{j=1..n+1} (1-q^(2j-1))/(1-q) for n>0, with T(0,0)=1. |
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+0
5
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| 1, 1, 1, 1, 3, 1, 1, 12, 12, 1, 1, 45, 97, 45, 1, 1, 170, 696, 696, 170, 1, 1, 644, 4784, 8447, 4784, 644, 1, 1, 2451, 32230, 92003, 92003, 32230, 2451, 1, 1, 9365, 214978, 946330, 1487477, 946330, 214978, 9365, 1, 1, 35908, 1426566, 9417798, 21856230, 21856230
(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) = A128080(n+1,nk+k) where A128080 is the triangle of coefficients of q in the q-analog of the odd double factorials.
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 3, 1;
1, 12, 12, 1;
1, 45, 97, 45, 1;
1, 170, 696, 696, 170, 1;
1, 644, 4784, 8447, 4784, 644, 1;
1, 2451, 32230, 92003, 92003, 32230, 2451, 1;
1, 9365, 214978, 946330, 1487477, 946330, 214978, 9365, 1;
1, 35908, 1426566, 9417798, 21856230, 21856230, 9417798, 1426566, 35908, 1;
1, 138104, 9441417, 91852376, 302951392, 441170745, 302951392, 91852376, 9441417, 138104, 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, (1-q^(2*j-1))/(1-q)), (n+1)*k, q)))}
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CROSSREFS
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Cf. A128080; A001147 ((2n-1)!!); A128593 (column 1), A128594 (column 2), A128595 (row sums); variant: A128596.
Sequence in context: A134523 A098778 A078122 this_sequence A129619 A094573 A055154
Adjacent sequences: A128589 A128590 A128591 this_sequence A128593 A128594 A128595
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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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