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A019465 Multiply by 1, add 1, multiply by 2, add 2, etc., start with 2.

%I A019465 #24 Feb 26 2018 04:16:23
%S A019465 2,2,3,6,8,24,27,108,112,560,565,3390,3396,23772,23779,190232,190240,
%T A019465 1712160,1712169,17121690,17121700,188338700,188338711,2260064532,
%U A019465 2260064544,29380839072,29380839085,411331747190,411331747204,6169976208060,6169976208075,98719619329200
%N A019465 Multiply by 1, add 1, multiply by 2, add 2, etc., start with 2.
%H A019465 Robert Israel, <a href="/A019465/b019465.txt">Table of n, a(n) for n = 0..898</a>
%F A019465 From _Robert Israel_, Dec 22 2015: (Start)
%F A019465 a(2*k) = 2*k! + Sum_{j=0..k-1} k!/j! =  2*k! + k*e*Gamma(k,1).
%F A019465 a(2*k+1) = 2*(k+1)! + Sum_{j=0..k-1} (k+1)!/j! = 2*(k+1)! + k*(k+1)*e*Gamma(k,1).
%F A019465 a(n) ~ (e+2)*(ceiling(n/2))!.  (End)
%p A019465 A[0]:= 2:
%p A019465 for n from 0 to 14 do
%p A019465   A[2*n+1]:= (n+1)*A[2*n];
%p A019465   A[2*n+2]:= (n+1)+A[2*n+1];
%p A019465 od:
%p A019465 seq(A[i],i=0..30); # _Robert Israel_, Dec 22 2015
%t A019465 a = {2}; Do[If[EvenQ@ Length@ a, AppendTo[a, Floor[Length[a]/2] Last@ a],
%t A019465 AppendTo[a, Last@ a + Floor[Length[a] /2]]], {k, 27}]; Rest@ a (* _Michael De Vlieger_, Dec 22 2015 *)
%o A019465 (PARI) A019465(n,a=2)={for(i=2,n+1,if(bittest(i,0),a+=i\2,a*=i\2));a} \\ _M. F. Hasler_, Feb 25 2018
%Y A019465 Cf. A082458 (same, but start with 0), A019465 (start with 2), A019466 (start with 3).
%Y A019465 Cf. A019460 .. A019463 & A082448 (similar, but first add, then multiply).
%K A019465 nonn,easy
%O A019465 0,1
%A A019465 _N. J. A. Sloane_
%E A019465 Edited by _M. F. Hasler_, Feb 25 2018