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A262842 G.f.: Product_{k>=1} (1 - x^k)^(-k^(k-2)).

%I A262842 #6 Oct 03 2015 16:07:16
%S A262842 1,1,2,5,22,150,1469,18452,282426,5088276,105431378,2469403421,
%T A262842 64508609896,1859464257187,58625171707730,2006861834895431,
%U A262842 74128128916520263,2938711927441481562,124457492116819509679,5607967808192795374759,267883606645817181302028,13522287374792657280601627,719232962773594118661491002,40204966834965724305054746851
%N A262842 G.f.: Product_{k>=1} (1 - x^k)^(-k^(k-2)).
%F A262842 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} d^(d-1) ).
%F A262842 Logarithmic derivative equals A262843, where A262843(n) = Sum_{d|n} d^(d-1).
%e A262842  G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 22*x^4 + 150*x^5 + 1469*x^6 +...
%e A262842 where
%e A262842 A(x) = 1/((1-x)*(1-x^2)*(1-x^3)^3*(1-x^4)^16*(1-x^5)^125*(1-x^6)^1296*...)
%e A262842 also
%e A262842 log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 67*x^4/4 + 626*x^5/5 + 7788*x^6/6 + 117650*x^7/7 + 2097219*x^8/8 + 43046731*x^9/9 + 1000000628*x^10/10 +...+ A262843(n)*x^n/n +...
%o A262842 (PARI) {a(n)=polcoeff(prod(k=1, n, (1 - x^k +x*O(x^n))^(-k^(k-2))), n)}
%o A262842 for(n=0,30,print1(a(n),", "))
%o A262842 (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, d^d)*x^m/m) +x*O(x^n)), n)}
%o A262842 for(n=0,30,print1(a(n),", "))
%Y A262842 Cf. A262843, A023879.
%K A262842 nonn
%O A262842 0,3
%A A262842 _Paul D. Hanna_, Oct 03 2015