A363481 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(2*x^k) * x^k/k ).
1, 2, 11, 108, 1969, 67542, 4473663, 582167944, 150236569819, 77226088637142, 79235069050108841, 162432444097491547308, 665648716390456030366881, 5454326724964994060395500598, 89374602386639273949112262243227
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..80
Programs
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PARI
seq(n) = my(A=1); for(i=1, n, A=exp(2*sum(k=1, i, subst(A, x, 2*x^k)*x^k/k)+x*O(x^n))); Vec(A);
Formula
A(x) = B(x)^2 where B(x) is the g.f. of A363480.
A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(k+1))^(2^(k+1) * a(k)).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 2^d * a(d-1) ) * a(n-k).