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A301624 G.f. A(x) satisfies: A(x) = Product_{k>=1} (1 - x^k*A(x)^k)^k.

%I A301624 #20 Feb 23 2020 16:09:43
%S A301624 1,-1,-1,4,1,-17,-6,118,-8,-876,625,5966,-7486,-41937,75969,306312,
%T A301624 -768637,-2164992,7487063,14461466,-70259884,-89410774,646971980,
%U A301624 459817892,-5861484630,-1128608133,52082250637,-15894742662,-453574650852,366848121166,3866670213663,-5215687717614
%N A301624 G.f. A(x) satisfies: A(x) = Product_{k>=1} (1 - x^k*A(x)^k)^k.
%F A301624 From _Peter Bala_, Feb 09 2020: (Start)
%F A301624 A(x) = 1/x * series reversion of ( exp( Sum_{n >= 1} sigma_2(n)*x^n/n ) ), where sigma_2(n) = A001157(n).
%F A301624 Equivalently, the o.g.f. A(x) satisfies [x^n](1/A(x))^n = sigma_2(n) for n >= 1. Cf. A066398. (End)
%F A301624 A(x) equals (1/x) * series reversion of (x * the o.g.f. for the sequence of planar partitions A000219).  - _Peter Bala_, Feb 11 2020
%e A301624 G.f. A(x) = 1 - x - x^2 + 4*x^3 + x^4 - 17*x^5 - 6*x^6 + 118*x^7 - 8*x^8 - 876*x^9 + 625*x^10 + ...
%e A301624 G.f. A(x) satisfies: A(x) = (1 - x*A(x)) * (1 - x^2*A(x)^2)^2 * (1 - x^3*A(x)^3)^3 * (1 - x^4*A(x)^4)^4 * ...
%e A301624 log(A(x)) = -x - 3*x^2/2 + 8*x^3/3 + 13*x^4/4 - 51*x^5/5 - 120*x^6/6 + 538*x^7/7 + 781*x^8/8 - 5419*x^9/9 - 3053*x^10/10 + ... + A281267(n)*x^n/n + ...
%p A301624 with(numtheory):
%p A301624 Order := 33:
%p A301624 Gser := solve(series(x*exp(add(sigma[2](n)*x^n/n, n = 1..32)), x) = y, x):
%p A301624 seq(coeff(Gser, y^k), k = 1..32); # _Peter Bala_, Feb 09 2020
%Y A301624 Cf. A000219, A006195, A066398, A073592, A109085, A181315, A278428, A281267, A301455, A301456, A301625.
%K A301624 sign
%O A301624 0,4
%A A301624 _Ilya Gutkovskiy_, Mar 24 2018