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A198242
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G.f.: q-Cosh(x) evaluated at q=-x.
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6
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1, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, 2, 3, 2, 1, 2, 4, 5, 5, 5, 5, 4, 1, -3, -5, -4, -2, -1, -3, -9, -15, -16, -14, -15, -21, -29, -33, -26, -7, 12, 14, -3, -21, -22, -7, 9, 16, 17, 20, 31, 52, 75, 84, 76, 72, 92, 124, 131, 91, 27, -8, 18, 83, 132, 127, 81, 46, 55
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OFFSET
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0,12
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COMMENTS
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Note: q-Cosh(x) = Sum_{n>=0} x^(2*n) * q^(n*(2*n-1)) / Product_{k=1..2*n} (1-q^k)/(1-q).
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LINKS
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FORMULA
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G.f.: Sum_{n>=0} x^(2*n) * (-x)^(n*(2*n-1)) / Product_{k=1..2*n} (1-(-x)^k)/(1+x).
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EXAMPLE
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G.f.: 1 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9 + 2*x^11 + 3*x^12 +...
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PROG
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(PARI) {a(n)=local(Cosh_q=sum(k=0, sqrtint(n+4), (-x)^(k*(2*k-1))*x^(2*k)/(prod(j=1, 2*k, (1-(-x)^j)/(1+x)+x*O(x^n))))); polcoeff(Cosh_q, n)}
for(n=0, 81, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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