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A252848
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Decimal expansion of Sum_{n>0} Sum_{k=0..n} exp(k)/n! = e*(e^e - 1)/(e - 1).
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0
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2, 2, 3, 9, 1, 7, 1, 3, 1, 6, 8, 9, 4, 0, 2, 1, 7, 1, 1, 4, 4, 1, 3, 7, 7, 6, 9, 6, 3, 8, 8, 1, 7, 3, 1, 3, 2, 4, 9, 9, 2, 1, 6, 7, 2, 3, 3, 4, 4, 5, 1, 9, 4, 4, 7, 2, 8, 5, 1, 0, 9, 9, 1, 7, 2, 7, 9, 0, 6, 8, 9, 3, 4, 4, 9, 9, 8, 0, 5, 6, 1, 0
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OFFSET
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2,1
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COMMENTS
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Terms in the sum begin: 1 + (1 + e)/1 + (1 + e + e^2)/2 + (1 + e + e^2 + e^3)/6 + ... .
The largest term in the sum is at n = 2, where that term is 5.5536... .
The double sum converges to a similar algebraic form using any base for exponentiation. For instance, using Pi as the base shows the general closed form:
Pi*(e^Pi - e)/(Pi - 1), which equals 29.9584963... .
As the base approaches 1, the ratio converges to 2e = Sum_{n>0} Sum_{k=0..n} 1/n! = 5.43656... . See A019762.
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LINKS
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FORMULA
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e*(e^e - 1)/(e - 1).
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EXAMPLE
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22.391713168940217114413... .
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MATHEMATICA
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Sum[N[Sum[Exp[k]/n!, {k, 0, n}], 100], {n, 0, Infinity}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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