A136751 - OEIS

%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