E.g.f. A(x) = 1 + x + 4*x^2/2! + 39*x^3/3! + 688*x^4/4! + 18765*x^5/5! + 722016*x^6/6! + 37003267*x^7/7! + 2426725120*x^8/8! + ...
such that
A(x) = 1 + x*W(x,1) + x^2*W(x,2)^4 + x^3*W(x,3)^9 + x^4*W(x,4)^16 + x^5*W(x,5)^25 + x^6*W(x,6)^36 + ...
where series W(x,n) = exp( x*W(x,n)^n ) begin:
W(x,1) = 1 + x + 3*x^2/2! + 16*x^3/3! + 125*x^4/4! + 1296*x^5/5! + ...
W(x,2) = 1 + x + 5*x^2/2! + 49*x^3/3! + 729*x^4/4! + 14641*x^5/5! + ...
W(x,3) = 1 + x + 7*x^2/2! + 100*x^3/3! + 2197*x^4/4! + 65536*x^5/5! + ...
W(x,4) = 1 + x + 9*x^2/2! + 169*x^3/3! + 4913*x^4/4! + 194481*x^5/5! + ...
W(x,5) = 1 + x + 11*x^2/2! + 256*x^3/3! + 9261*x^4/4! + 456976*x^5/5! + ...
W(x,6) = 1 + x + 13*x^2/2! + 361*x^3/3! + 15625*x^4/4! + 923521*x^5/5! + ...
...
and series W(x,n)^n = Series_Reversion( x*exp(-n*x) ) / x begin:
W(x,1) = 1 + x + 3*x^2/2! + 16*x^3/3! + 125*x^4/4! + 1296*x^5/5! + ...
W(x,2)^2 = 1 + 2*x + 12*x^2/2! + 128*x^3/3! + 2000*x^4/4! + ...
W(x,3)^3 = 1 + 3*x + 27*x^2/2! + 432*x^3/3! + 10125*x^4/4! + ...
W(x,4)^4 = 1 + 4*x + 48*x^2/2! + 1024*x^3/3! + 32000*x^4/4! + ...
W(x,5)^5 = 1 + 5*x + 75*x^2/2! + 2000*x^3/3! + 78125*x^4/4! + ...
W(x,6)^6 = 1 + 6*x + 108*x^2/2! + 3456*x^3/3! + 162000*x^4/4! + ...
...
and series W(x,n)^(n^2) begin:
W(x,1) = 1 + x + 3*x^2/2! + 16*x^3/3! + 125*x^4/4! + 1296*x^5/5! + ...
W(x,2)^4 = 1 + 4*x + 32*x^2/2! + 400*x^3/3! + 6912*x^4/4! + ...
W(x,3)^9 = 1 + 9*x + 135*x^2/2! + 2916*x^3/3! + 83349*x^4/4! + ...
W(x,4)^16 = 1 + 16*x + 384*x^2/2! + 12544*x^3/3! + 524288*x^4/4! + ...
W(x,5)^25 = 1 + 25*x + 875*x^2/2! + 40000*x^3/3! + 2278125*x^4/4! + ...
W(x,6)^36 = 1 + 36*x + 1728*x^2/2! + 104976*x^3/3! + 7776000*x^4/4! + ...
...
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