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A104409
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Coefficients of the B-Rogers-Selberg identity.
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3
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1, 0, 0, 0, 1, -1, 1, -1, 2, -2, 2, -2, 4, -4, 4, -5, 7, -7, 8, -9, 12, -13, 14, -16, 21, -22, 24, -28, 34, -37, 41, -46, 55, -60, 66, -74, 87, -95, 104, -117, 135, -147, 162, -180, 205, -225, 246, -273, 309, -337, 369, -408, 457, -499, 546, -601, 669, -730, 796, -874, 969, -1055, 1149, -1259
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OFFSET
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0,9
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LINKS
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FORMULA
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Expansion of f(-q^2, -q^5) / f(-q^2) in powers of q where f() is Ramanujan's theta function.
Euler transform of period 14 sequence [ 0, 0, 0, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, ...]. - Michael Somos, Dec 04 2007
a(n) ~ (-1)^n * sin(Pi/7) * 11^(1/4) * exp(Pi*sqrt(11*n/42)) / (3^(1/4) * 14^(3/4) * n^(3/4)). - Vaclav Kotesovec, Oct 04 2015
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EXAMPLE
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1 + q^4 - q^5 + q^6 - q^7 + 2*q^8 - 2*q^9 + 2*q^10 + ...
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MATHEMATICA
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nmax=60; CoefficientList[Series[Product[(1-x^(7*k-2))*(1-x^(7*k-5))*(1-x^(7*k))/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 04 2015 *)
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PROG
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(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x*O(x^n))^[0, 0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 0, 0, 0][k%14+1]), n))} /* Michael Somos, Dec 04 2007 */
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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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