A385635 G.f. satisfies A(x) = x + Product_{n>=2} A(x^n) with A(0) = 1.

1, 1, 1, 1, 2, 2, 4, 4, 8, 8, 13, 15, 26, 26, 41, 48, 73, 80, 119, 136, 198, 225, 313, 367, 518, 585, 797, 941, 1264, 1466, 1953, 2285, 3022, 3524, 4571, 5391, 6993, 8152, 10440, 12316, 15684, 18370, 23236, 27327, 34389, 40364, 50370, 59292, 73880, 86547, 107080, 125976, 155266, 182058

Offset: 0

Author

Paul D. Hanna, Jul 05 2025

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 2*x^5 + 4*x^6 + 4*x^7 + 8*x^8 + 8*x^9 + 13*x^10 + 15*x^11 + 26*x^12 + ...
where
A(x) = x + A(x^2)*A(x^3)*A(x^4)*A(x^5)* ... * A(x^n) * ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..1024

Crossrefs

Cf. A129374, A129375.

Programs

PARI

{a(n) = my(A=1+x +x*O(x^n)); for(i=1, ceil(log(n+2)/log(2)), A = x + prod(k=2,#A,subst(A, x, x^k)) +x*O(x^n); ); polcoef(A, n)}
for(n=0, 50, print1(a(n), ", "))