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G.f. A(x) satisfies A(x) = 1 + Sum_{n>=1} A(x)^n * x^n*(1 + x^n)^n.
1

%I #10 Aug 24 2024 10:52:18

%S 1,1,3,7,23,71,245,844,3031,11023,40890,153456,582868,2234096,8634800,

%T 33607223,131619098,518285703,2050849866,8150520122,32519072805,

%U 130205541912,523022475545,2107119140699,8511959958494,34470547999253,139914333878668,569112388312690

%N G.f. A(x) satisfies A(x) = 1 + Sum_{n>=1} A(x)^n * x^n*(1 + x^n)^n.

%e G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 23*x^4 + 71*x^5 + 245*x^6 +...

%e where

%e A(x) = 1 + A(x)*x*(1+x) + A(x)^2*x^2*(1+x^2)^2 + A(x)^3*x^3*(1+x^3)^3 +...

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, A^m*x^m*(1+x^m+x*O(x^n))^m)); polcoeff(A, n)}

%Y Cf. A194690.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 01 2011