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A309080 Product minus sum of all previous terms in the sequence, starting with a(1) = 2 and a(2) = 5.

%I A309080 #20 Sep 01 2019 10:21:29
%S A309080 2,5,3,20,570,341400,116758458000,13632577445813641200000,
%T A309080 185847167817698504752014113195034069600000000,
%U A309080 34539169785859790805229099212216829464451540660176789302662465332580254227520000000000000
%N A309080 Product minus sum of all previous terms in the sequence, starting with a(1) = 2 and a(2) = 5.
%F A309080 a(n) = Product_{k=1..n-1} a(k) - Sum_{k=1..n-1} a(k) with a(1) = 2, a(2) = 5.
%e A309080 a(4) = a(1)*a(2)*a(3) - (a(1) + a(2) + a(3)) = 2*5*3 - (2 + 5 + 3) = 20.
%t A309080 x1 = 2; x2 = 5; p = x1 * x2; s = x1 + x2; x = p - s; A309080 = {x1, x2, x}; Do[p = p * x; s = s + x; x = p - s; AppendTo[A309080, x], {n, 16}]
%o A309080 (Python)
%o A309080 a, n, p, s = [2,5], 2, 2, 2
%o A309080 while n < 10:
%o A309080     p, s, n = p*a[len(a)-1], s+a[len(a)-1], n+1
%o A309080     a = a+[p-s]
%o A309080 for n in range(1, 11): print(a[n-1], end=', ') # _A.H.M. Smeets_, Aug 22 2019
%Y A309080 Cf. A123702.
%K A309080 nonn
%O A309080 1,1
%A A309080 _Christopher C. Capobianco_, Jul 11 2019