cp's OEIS Frontend

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

%I A385635 #9 Jul 06 2025 05:08:02
%S A385635 1,1,1,1,2,2,4,4,8,8,13,15,26,26,41,48,73,80,119,136,198,225,313,367,
%T A385635 518,585,797,941,1264,1466,1953,2285,3022,3524,4571,5391,6993,8152,
%U A385635 10440,12316,15684,18370,23236,27327,34389,40364,50370,59292,73880,86547,107080,125976,155266,182058
%N A385635 G.f. satisfies A(x) = x + Product_{n>=2} A(x^n) with A(0) = 1.
%H A385635 Paul D. Hanna, <a href="/A385635/b385635.txt">Table of n, a(n) for n = 0..1024</a>
%e A385635 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 + ...
%e A385635 where
%e A385635 A(x) = x + A(x^2)*A(x^3)*A(x^4)*A(x^5)* ... * A(x^n) * ...
%o A385635 (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)}
%o A385635 for(n=0, 50, print1(a(n), ", "))
%Y A385635 Cf. A129374, A129375.
%K A385635 nonn
%O A385635 0,5
%A A385635 _Paul D. Hanna_, Jul 05 2025