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A128593
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Column 1 of triangle A128592; a(n) = coefficient of q^(n+2) in the q-analog of the odd double factorials (2n+3)!! for n>=0.
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5
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1, 3, 12, 45, 170, 644, 2451, 9365, 35908, 138104, 532589, 2058782, 7975216, 30951921, 120326060, 468473348, 1826415556, 7129330988, 27860219331, 108984557708, 426730087879, 1672310507262, 6558840830680, 25742937514814, 101108341344396, 397368218111003
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = [q^(n+2)] Product_{j=1..n+2} (1-q^(2j-1))/(1-q) for n>=0.
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1,
simplify(b(n-1)*(1-q^(2*n-1))/(1-q)))
end:
a:= n-> coeff(b(n+2), q, n+2):
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MATHEMATICA
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a[n_] := SeriesCoefficient[Product[(1-q^(2j-1))/(1-q), {j, 1, n+2}], {q, 0, n+2}];
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PROG
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(PARI) {a(n)=polcoeff(prod(j=1, n+2, (1-q^(2*j-1))/(1-q)), n+2, q)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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