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A319360
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Expansion of e.g.f. (1 + x)*exp(log(1 + x)^2/2).
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1
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1, 1, 1, 0, 2, -10, 64, -476, 4038, -38466, 406446, -4716624, 59621748, -815339460, 11992028112, -188746844040, 3165161922492, -56333871521508, 1060525150393308, -21053827255670976, 439558554065307288, -9627439778044075512, 220722057792327097920, -5286159770781782374800
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OFFSET
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0,5
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COMMENTS
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Inverse Stirling transform of A000085.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Stirling1(n,k)*A000085(k).
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MAPLE
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seq(n!*coeff(series((1 + x)*exp(log(1 + x)^2/2), x=0, 24), x, n), n=0..23); # Paolo P. Lava, Jan 09 2019
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MATHEMATICA
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nmax = 23; CoefficientList[Series[(1 + x) Exp[Log[1 + x]^2/2], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] HypergeometricU[-k/2, 1/2, -1/2]/(-1/2)^(k/2), {k, 0, n}], {n, 0, 23}]
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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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