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A244519 Expansion of Product_{n>=1} (1 + H(x^n)) where H(x) is the g.f. of A000081.

%I A244519 #9 Oct 13 2017 21:36:56
%S A244519 1,1,2,4,8,16,35,76,175,414,1009,2510,6382,16448,42961,113352,301715,
%T A244519 808932,2182739,5921803,16143975,44199809,121477237,335015538,
%U A244519 926814691,2571322157,7152404733,19942874638,55729271645,156051344975,437801148097,1230423785329,3463777894236,9766002585763,27574869734583,77965430442158
%N A244519 Expansion of Product_{n>=1} (1 + H(x^n)) where H(x) is the g.f. of A000081.
%C A244519 Which combinatorial objects does this sequence count?
%H A244519 Joerg Arndt, <a href="/A244519/b244519.txt">Table of n, a(n) for n = 0..500</a>
%o A244519 (PARI)
%o A244519 N=66;  A=vector(N+1, j, 1);
%o A244519 for (n=1, N, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d * A[d]) * A[n-k+1] ) );
%o A244519 A000081=concat([0], A);
%o A244519 H(t)=subst(Ser(A000081, 't), 't, t);
%o A244519 x='x+O('x^N);
%o A244519 T=prod(n=1,N, 1 + H(x^n));
%o A244519 Vec(T)
%Y A244519 Cf. A001372 (expansion of 1/Product_{n>=1} (1 - H(x^n))).
%K A244519 nonn
%O A244519 0,3
%A A244519 _Joerg Arndt_, Jul 10 2014