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A326856
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E.g.f.: Product_{k>=1} (1 + x^(4*k-3) / (4*k-3)).
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3
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1, 1, 0, 0, 0, 24, 144, 0, 0, 40320, 403200, 0, 0, 479001600, 8643317760, 29059430400, 0, 20922789888000, 475108274995200, 1871463083212800, 0, 2432902008176640000, 76354225980899328000, 525098781423304704000, 0, 620448401733239439360000
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OFFSET
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0,6
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COMMENTS
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In general, if c > 0, mod(d,c) <> 0 and e.g.f. = Product_{k>=1} (1 + x^(c*k+d) / (c*k+d)), then a(n) ~ n! * Gamma(1 + d/c) / (c^(1/c) * exp(gamma/c) * Gamma(1/c) * Gamma(1 + (d+1)/c) * n^(1 - 1/c)), where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the Gamma function.
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LINKS
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FORMULA
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a(n) ~ n! / (sqrt(2*Pi) * exp(gamma/4) * n^(3/4)), where gamma is the Euler-Mascheroni constant A001620.
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MATHEMATICA
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nmax = 30; CoefficientList[Series[Product[(1+x^(4*k-3)/(4*k-3)), {k, 1, Floor[nmax/4]+1}], {x, 0, nmax}], x] * Range[0, nmax]!
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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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