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A255169
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Decimal expansion of the sum_{n>=0} n^2/e^n = e(1+e)/(e-1)^3.
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2
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1, 9, 9, 2, 2, 9, 4, 7, 6, 7, 1, 2, 4, 9, 8, 7, 3, 9, 2, 9, 2, 6, 0, 1, 6, 6, 1, 3, 0, 0, 2, 1, 1, 7, 3, 8, 7, 8, 3, 1, 4, 0, 4, 5, 2, 3, 0, 6, 3, 7, 7, 0, 0, 6, 9, 5, 2, 3, 5, 0, 1, 6, 8, 4, 8, 4, 8, 1, 9, 8, 9, 9, 3, 4, 9, 7, 9, 2, 7, 0, 5, 8
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OFFSET
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1,2
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COMMENTS
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The expression generating this constant is a second degree Eulerian polynomial, in the "variable" e, with coefficients {1, 1}, generated from sum_{n>=0} n^m/e^n, with m=2. See A008292. It approximates m!.
See A098875 for the first degree polynomial and value.
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LINKS
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FORMULA
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Equals sum_{n>=0} n^2/e^n.
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EXAMPLE
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1.99229476712498....
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MATHEMATICA
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Sum[n^2/Exp[n], {n, 0, Infinity}]; N[Sum[n^2/Exp[n], {n, 0, Infinity}], 100]
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PROG
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(PARI) exp(1)*(1+exp(1))/(exp(1)-1)^3 \\ Altug Alkan, Jul 30 2018
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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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