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%I #32 Oct 30 2018 09:43:58
%S 1,1,2,2,6,24,36,20736,20808,8947059130368,8947059171984,
%T 716210897494804754044764041567551881216,
%U 716210897494804754044764059461670225184
%N a(0) = 1; if n is odd, a(n) = Product_{i=0..n-1} a(i); if n is even, a(n) = Sum_{i=0..n-1} a(i).
%C Next term is too large to include.
%C Odd terms are the product of previous terms and even terms are the sum of previous terms.
%H Iain Fox, <a href="/A320603/b320603.txt">Table of n, a(n) for n = 0..18</a>
%H Iain Fox, <a href="/A320603/a320603.txt">Table of n, a(n) for n = 0..32</a>
%F a(n) = a(n-1) + 2*a(n-2), for even n > 2.
%F a(n) = a(n-1) * a(n-2)^2, for odd n > 1.
%e 5 is odd, so a(5) = 1 * 1 * 2 * 2 * 6 = 24.
%e 6 is even, so a(6) = 1 + 1 + 2 + 2 + 6 + 24 = 36.
%t a[0]:= 1; a[n_]:= If[OddQ[n], Product[a[j], {j,0,n-1}], Sum[a[j], {j,0,n -1}]]; Table[a[n], {n, 0, 15}] (* _G. C. Greubel_, Oct 19 2018 *)
%o (PARI) first(n) = my(res = vector(n, i, 1)); for(x=3, n, res[x]=if(x%2, sum(i=1, x-1, res[i]), prod(i=1, x-1, res[i]))); res
%o (PARI) first(n) = my(res = vector(n, i, 1)); res[3]++; for(x=4, n, res[x]=if(x%2, res[x-1]+2*res[x-2], res[x-1]*res[x-2]^2)); res
%Y Cf. A039941, A077753, A122961.
%Y Sum of previous terms: A011782.
%Y Product of previous terms: A165420.
%K nonn
%O 0,3
%A _Iain Fox_, Oct 17 2018