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Floor[Accumulate[FractionalPart[2 Range[80]E]]] (* Harvey P. Dale, Aug 16 2021 *)

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a(n) = [sumSum_{k=1..n} (2k*e) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.

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a(n) = [sum{(2k*e) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.

(PARI) a(n) = floor(sum(k=1, n, frac(2*exp(1)*k))); \\ Michel Marcus, Nov 12 2017

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G. C. Greubel, <a href="/A194202/b194202.txt">Table of n, a(n) for n = 1..5000</a>

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_Clark Kimberling (ck6(AT)evansville.edu), _, Aug 19 2011