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%I #9 Jul 14 2019 06:26:19
%S 1,2,6,18,50,143,397,1088,2973,8093,22014,59861,162742,442396,1202589,
%T 3268996,8886090,24154933,65659949,178482278,485165168,1318815708,
%U 3584912818,9744803414,26489122097,72004899306,195729609397,532048240570,1446257064252
%N a(n) = Sum_{k >= 0} floor(n^k / k!).
%C This sequence is inspired by the Maclaurin series for the exponential function.
%C The series in the name is well defined; for any n > 0, only the first A065027(n) terms are different from zero.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Taylor_series#Exponential_function">Taylor series: Exponential function</a>
%F a(n) ~ exp(n) as n tends to infinity.
%F a(n) <= A000149(n).
%F a(n) = A309104(n) + A309105(n).
%e For n = 3:
%e - we have:
%e k floor(3^k / k!)
%e - ---------------
%e 0 1
%e 1 3
%e 2 4
%e 3 4
%e 4 3
%e 5 2
%e 6 1
%e >=7 0
%e - hence a(3) = 1 + 3 + 4 + 4 + 3 + 2 + 1 = 18.
%o (PARI) a(n) = { my (v=0, d=1); for (k=1, oo, if (d<1, return (v), v += floor(d); d *= n/k)) }
%Y See A309103, A309104, A309105 for similar sequences.
%Y Cf. A000149, A065027.
%K nonn
%O 0,2
%A _Rémy Sigrist_, Jul 11 2019
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