A363427 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(4*x^k) * x^k/k ).
1, 1, 4, 68, 4422, 1136646, 1165077220, 4773325045092, 78210934437541505, 5125710024629047469249, 1343679254641311248179226112, 1408951161809404147369817577873792, 5909570902737024213107077083032728540592
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..58
Programs
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PARI
seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, 4*x^k)*x^k/k)+x*O(x^n))); Vec(A);
Formula
A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+x^(k+1))^(4^k * a(k)).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d * 4^(d-1) * a(d-1) ) * a(n-k).