A362389 G.f. satisfies A(x) = exp( Sum_{k>=1} (2^k + A(x^k)) * x^k/k ).
1, 3, 10, 34, 122, 450, 1723, 6758, 27135, 110913, 460395, 1935233, 8222504, 35255000, 152353021, 662892684, 2901595559, 12768195617, 56450822365, 250637657015, 1117060889815, 4995815027658, 22413020866875, 100842092305575, 454912716037387
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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PARI
seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (2^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
Formula
A(x) = B(x)/(1 - 2*x) where B(x) is the g.f. of A363545.
A(x) = Sum_{k>=0} a(k) * x^k = 1/(1-2*x) * 1/Product_{k>=0} (1-x^(k+1))^a(k).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 2^k + Sum_{d|k} d * a(d-1) ) * a(n-k).