A145386 - OEIS

%I #10 Mar 28 2018 04:55:26

%S 1,3,21,567,326025,106295560875,11298746263006377496125,

%T 127661667115800580590177504581888913674961375

%N a(1) = 1; a(n) = a(n-1)*(2*(n-1)+a(n-1)) for n > 1.

%C Next term has 89 decimal digits and is too large to include. - _Klaus Brockhaus_, Oct 13 2008

%F a(n) = Product_{k = 1..n} b(k), where b(1) = 1 and b(n) = a(n-1) + 2*(n-1) for n > 1. The sequence b(n) begins [1, 3, 7, 27, 575, 326035, ...] and is given by the recurrence b(n) = b(n-1)^2 - 2*(n-2)*b(n-1) + 2*(n-1) with b(1) = 1. - _Peter Bala_, Mar 27 2018

%e a(2) = a(1)*(2*(2-1)+a(1)) = 1*(2*1+1) = 3. - _Klaus Brockhaus_, Oct 13 2008

%t lst={};s=1;Do[s*=(n+=s+n);AppendTo[lst,s],{n,0,7}];lst

%o (ARIBAS) a:=1; for n:=1 to 9 do a:=a*(a+2*(n-1)); write(a:group(0), ","); end; end; (* _Klaus Brockhaus_, Oct 13 2008 *)

%o (PARI) a=vector(15); a[1]=1; for(n=2, #a, a[n] = a[n-1]*(2*(n-1)+a[n-1])); a \\ _Altug Alkan_, Mar 27 2018

%K nonn,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Oct 10 20

%E Name edited by _Klaus Brockhaus_, Oct 13 2008