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A269700 a(n) = floor( Product_{k>=0} (1 + n/k!) ).

%I A269700 #15 Apr 07 2016 13:24:26
%S A269700 1,7,26,69,151,293,519,862,1361,2062,3019,4297,5969,8121,10848,14261,
%T A269700 18481,23646,29908,37437,46419,57061,69586,84242,101297,121042,143793,
%U A269700 169893,199710,233642,272117,315592,364560,419545,481109,549849,626403,711448,805703
%N A269700 a(n) = floor( Product_{k>=0} (1 + n/k!) ).
%H A269700 Daniel Suteu, <a href="/A269700/b269700.txt">Table of n, a(n) for n = 0..500</a>
%e A269700 For n=3, a(3) = floor(69.52294621467075235981513247145953...) = 69.
%t A269700 Table[Floor@ Product[1 + n/k!, {k, 0, 10^2}], {n, 0, 38}] (* _Michael De Vlieger_, Mar 27 2016 *)
%o A269700 (Sidef)
%o A269700 func a(n) {
%o A269700     var (prod=1, prev=1)
%o A269700     for i in (0 ..^ Inf) {
%o A269700         prod *= (1 + n/i!)
%o A269700         break if (prod/prev <= 1+1e-100)
%o A269700         prev = prod
%o A269700     }
%o A269700     return floor(prod)
%o A269700 }
%o A269700 range(0, 100).each { |n| say a(n) }
%o A269700 (PARI) a(n) = floor(prodinf(k=0, 1+n/k!)); \\ _Michel Marcus_, Mar 04 2016
%Y A269700 Cf. A238695.
%K A269700 nonn,easy
%O A269700 0,2
%A A269700 _Daniel Suteu_, Mar 03 2016