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

%I #9 Oct 13 2017 21:36:56

%S 1,1,2,4,8,16,35,76,175,414,1009,2510,6382,16448,42961,113352,301715,

%T 808932,2182739,5921803,16143975,44199809,121477237,335015538,

%U 926814691,2571322157,7152404733,19942874638,55729271645,156051344975,437801148097,1230423785329,3463777894236,9766002585763,27574869734583,77965430442158

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

%C Which combinatorial objects does this sequence count?

%H Joerg Arndt, <a href="/A244519/b244519.txt">Table of n, a(n) for n = 0..500</a>

%o (PARI)

%o N=66; A=vector(N+1, j, 1);

%o for (n=1, N, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d * A[d]) * A[n-k+1] ) );

%o A000081=concat([0], A);

%o H(t)=subst(Ser(A000081, 't), 't, t);

%o x='x+O('x^N);

%o T=prod(n=1,N, 1 + H(x^n));

%o Vec(T)

%Y Cf. A001372 (expansion of 1/Product_{n>=1} (1 - H(x^n))).

%K nonn

%O 0,3

%A _Joerg Arndt_, Jul 10 2014

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