A122961 Alternately form product and sum of all previous terms.

1, 1, 1, 3, 3, 9, 81, 99, 649539, 649737, 274124633198656977, 274124633199956451, 20598907656583661830059012023854018733151994905840579, 20598907656583661830059012023854019281401261305753481

Offset: 1

Author

Franklin T. Adams-Watters, Oct 26 2006

Keywords

• nonn

Comments

Note that definition does not make a(1) a special case; it is the empty product, which is 1. If we started with addition, the sequence would be all zeros.

Links

• Iain Fox, Table of n, a(n) for n = 1..18
• Iain Fox, Table of n, a(n) for n = 1..34

Crossrefs

Cf. A039941, A000004, A320603.

Programs

PARI

first(n) = my(res = vector(n, i, 1)); for(x=4, n, res[x]=if(x%2, prod(i=1, x-1, res[i]), sum(i=1, x-1, res[i]))); res \\ Iain Fox, Oct 29 2018

PARI

first(n) = my(res = vector(n, i, 1)); for(x=4, n, res[x]=if(x%2, res[x-1]*res[x-2]^2, res[x-1]+2*res[x-2])); res \\ Iain Fox, Oct 29 2018

Formula

a(1) = a(2) = 1. For n > 1, a(2n-1) = a(2n-3)^2 * a(2n-2), a(2n) = 2 * a(2n-2) + a(2n-1).