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A370735
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a(n) = 5^(2*n) * [x^n] Product_{k>=1} 1/(1 - 3*x^k)^(1/5).
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3
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1, 15, 1050, 52125, 3277500, 179801250, 11966690625, 738318187500, 49788716718750, 3314446448437500, 227432073022265625, 15631633385109375000, 1090877899335878906250, 76338563689129101562500, 5384934139819611328125000, 381204340327212964599609375, 27111589537137988341064453125
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OFFSET
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0,2
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COMMENTS
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In general, if d > 1, m >= 1 and g.f. = Product_{k>=1} 1/(1 - d*x^k)^(1/m), then a(n) ~ d^n / (Gamma(1/m) * QPochhammer(1/d)^(1/m) * n^(1 - 1/m)).
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LINKS
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FORMULA
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G.f.: Product_{k>=1} 1/(1 - 3*(25*x)^k)^(1/5).
a(n) ~ 75^n / (Gamma(1/5) * QPochhammer(1/3)^(1/5) * n^(4/5)).
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MATHEMATICA
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nmax = 20; CoefficientList[Series[Product[1/(1-3*x^k), {k, 1, nmax}]^(1/5), {x, 0, nmax}], x] * 25^Range[0, nmax]
nmax = 20; CoefficientList[Series[Product[1/(1-3*(25*x)^k), {k, 1, nmax}]^(1/5), {x, 0, nmax}], x]
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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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