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A300621
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Numerators of sequence whose exponential self-convolution yields sequence 1, 2, 3, 5, 7, 11, 13, ... (1 with primes).
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1
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1, 1, 1, 1, -5, 27, -277, 895, -27655, 248185, -5052519, 28731489, -1444496477, 19885473347, -595129566605, 4808968469791, -333894246376015, 6195249562217393, -244725707175834895, 2563206341379247681, -227039228335442728053, 5299214394077195384747, -260053313429315175721413
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OFFSET
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0,5
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LINKS
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FORMULA
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Numerators of coefficients in expansion of e.g.f. sqrt(1 + Sum_{k>=1} prime(k)*x^k/k!).
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EXAMPLE
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1, 1, 1/2, 1, -5/4, 27/4, -277/8, 895/4, -27655/16, 248185/16, -5052519/32, 28731489/16, -1444496477/64, 19885473347/64, ...
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MATHEMATICA
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Numerator[nmax = 22; CoefficientList[Series[(1 + Sum[Prime[k] x^k/k!, {k, 1, nmax}])^(1/2), {x, 0, nmax}], x] Range[0, nmax] !]
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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