A320603 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).

1, 1, 2, 2, 6, 24, 36, 20736, 20808, 8947059130368, 8947059171984, 716210897494804754044764041567551881216, 716210897494804754044764059461670225184

Offset: 0

Author

Iain Fox, Oct 17 2018

Keywords

• nonn

Comments

Next term is too large to include.

Odd terms are the product of previous terms and even terms are the sum of previous terms.

Examples

			5 is odd, so a(5) = 1 * 1 * 2 * 2 * 6 = 24.
6 is even, so a(6) = 1 + 1 + 2 + 2 + 6 + 24 = 36.
		

Links

• Iain Fox, Table of n, a(n) for n = 0..18
• Iain Fox, Table of n, a(n) for n = 0..32

Crossrefs

Cf. A039941, A077753, A122961.

Sum of previous terms: A011782.

Product of previous terms: A165420.

Programs

Mathematica

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 *)

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

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

Formula

a(n) = a(n-1) + 2*a(n-2), for even n > 2.

a(n) = a(n-1) * a(n-2)^2, for odd n > 1.