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%I #12 Jun 05 2021 01:46:59
%S 1,1,2,5,13,36,104,310,943,2913,9112,28805,91893,295484,956671,
%T 3115805,10200445,33544983,110755143,366976365,1219814018,4066305982,
%U 13590864072,45534416250,152895704998,514446539489,1734239511881
%N G.f.: A(x) = ...o x/(1-x^4) o x/(1-x^3) o x/(1-x^2) o x/(1-x), composition of functions x/(1-x^n) for n = 1,2,3,...
%C The composition transpose of A136750.
%e G.f.: A(x) is the limit of composition of functions x/(1-x^n):
%e F_1(x) = x/(1-x)
%e F_2(x) = x/(1-x^2) o F_1(x) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 +...
%e F_3(x) = x/(1-x^3) o F_2(x) = x + x^2 + 2x^3 + 5x^4 + 12x^5 + 30x^6 +...
%e F_4(x) = x/(1-x^4) o F_3(x) = x + x^2 + 2x^3 + 5x^4 + 13x^5 + 35x^6 +...
%e F_5(x) = x/(1-x^5) o F_4(x) = x + x^2 + 2x^3 + 5x^4 + 13x^5 + 36x^6 +...
%e F_6(x) = x/(1-x^6) o x/(1-x^5) o x/(1-x^4) o x/(1-x^3) o x/(1-x^2) o x/(1-x) =
%e x + x^2 + 2*x^3 + 5*x^4 + 13*x^5 + 36*x^6 + 104*x^7 + 309*x^8 + 934*x^9 + ...
%o (PARI) {a(n)=local(A=x+x*O(x^n));if(n<=0,0,for(i=1,n,A=A/(1-A^i));polcoeff(A,n))}
%o for(n=1,40,print1(a(n),", "))
%Y Cf. A136750; variants: A136752, A136753, A119470, A119471.
%Y Cf. A064580. - _Gary W. Adamson_, Jun 21 2009
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 21 2008
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