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A360707
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G.f.: Sum_{k>=0} (1 + k*x)^k * x^(3*k).
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5
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1, 0, 0, 1, 1, 0, 1, 4, 4, 1, 9, 27, 28, 16, 96, 257, 281, 250, 1251, 3161, 3665, 4321, 19489, 47685, 58662, 84099, 354739, 852216, 1110344, 1837924, 7401269, 17604002, 24221890, 44761045, 174287005, 412627144, 597640105, 1204831674, 4574415066, 10818841343
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OFFSET
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0,8
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} binomial(k,n-3*k) * k^(n-3*k).
log(a(n)) ~ n/4 * log(n/4).
a(n) ~ exp(exp(1/4)*n^(1/4)/4^(1/4)) * n^(n/4) / 4^(n/4 + 1) * (1 + 1/(2^(5/2)*exp(1/4)*n^(1/4)) + (67/(192*exp(1/2)) - 15*exp(1/2)/16)/sqrt(n)).
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MATHEMATICA
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nmax = 50; CoefficientList[Series[Sum[(1 + k*x)^k * x^(3*k), {k, 0, nmax}], {x, 0, nmax}], x]
Join[{1}, Table[Sum[Binomial[k, n - 3*k] * k^(n - 3*k), {k, 0, n}], {n, 1, 50}]]
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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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