A363423 G.f. satisfies A(x) = exp( Sum_{k>=1} A(3*x^k) * x^k/k ).
1, 1, 4, 40, 1126, 92440, 22559276, 16468584194, 36033333480881, 236450784546518006, 4654297351684653345788, 274836259327539399144691019, 48686693681325683653963188907344, 25874153864215746591981599665978198380
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..65
Programs
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PARI
seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, 3*x^k)*x^k/k)+x*O(x^n))); Vec(A);
Formula
A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(k+1))^(3^k * a(k)).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 3^(d-1) * a(d-1) ) * a(n-k).