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A303348
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Expansion of Product_{n>=1} (1 - 9*x^n)^(1/3).
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3
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1, -3, -12, -39, -246, -1578, -11487, -84054, -635781, -4893357, -38292969, -303553209, -2432865630, -19678331838, -160427322399, -1316796234933, -10872602692581, -90242886252945, -752488383572787, -6300541703215803, -52949782408528290
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OFFSET
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0,2
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COMMENTS
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This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1/3, g(n) = 9.
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LINKS
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FORMULA
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a(n) ~ -c * 3^(2*n-1) / (Gamma(2/3) * n^(4/3)), where c = QPochhammer[1/9]^(1/3) = 0.95703379660353017269195329... - Vaclav Kotesovec, Apr 25 2018
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MAPLE
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seq(coeff(series(mul((1-9*x^k)^(1/3), k=1..n), x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 22 2018
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-9*x^k)^(1/3)))
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CROSSREFS
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Expansion of Product_{n>=1} (1 - b^2*x^n)^(1/b): A010815 (b=1), A303347 (b=2), this sequence (b=3).
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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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