A136751
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,...
Original entry on oeis.org
1, 1, 2, 5, 13, 36, 104, 310, 943, 2913, 9112, 28805, 91893, 295484, 956671, 3115805, 10200445, 33544983, 110755143, 366976365, 1219814018, 4066305982, 13590864072, 45534416250, 152895704998, 514446539489, 1734239511881
Offset: 0
G.f.: A(x) is the limit of composition of functions x/(1-x^n):
F_1(x) = x/(1-x)
F_2(x) = x/(1-x^2) o F_1(x) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 +...
F_3(x) = x/(1-x^3) o F_2(x) = x + x^2 + 2x^3 + 5x^4 + 12x^5 + 30x^6 +...
F_4(x) = x/(1-x^4) o F_3(x) = x + x^2 + 2x^3 + 5x^4 + 13x^5 + 35x^6 +...
F_5(x) = x/(1-x^5) o F_4(x) = x + x^2 + 2x^3 + 5x^4 + 13x^5 + 36x^6 +...
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) =
x + x^2 + 2*x^3 + 5*x^4 + 13*x^5 + 36*x^6 + 104*x^7 + 309*x^8 + 934*x^9 + ...
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{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))}
for(n=1,40,print1(a(n),", "))
A136750
G.f.: A(x) = x/(1-x) o x/(1-x^2) o x/(1-x^3) o x/(1-x^4) o..., composition of functions x/(1-x^n) for n = ...,3,2,1.
Original entry on oeis.org
1, 1, 2, 4, 8, 17, 35, 74, 155, 329, 692, 1464, 3098, 6553, 13873, 29361, 62165, 131638, 278787, 590357, 1250337, 2648108, 5608735, 11879607, 25161906, 53295451, 112886028, 239108343, 506466366, 1072776347, 2272316123, 4813150684
Offset: 0
G.f.: A(x) is the limit of composition of functions x/(1-x^n):
F_1(x) = x/(1-x)
F_2(x) = F_1(x/(1-x^2)) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8*x^6 + 13x^7 +...
F_3(x) = F_2(x/(1-x^3)) = x + x^2 + 2x^3 + 4x^4 + 7x^5 + 14x^6 + 26x^7 +...
F_4(x) = F_3(x/(1-x^4)) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 + 32x^7 +...
F_5(x) = F_4(x/(1-x^5)) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 17x^6 + 34x^7 +...
F_6(x) = x/(1-x) o x/(1-x^2) o x/(1-x^3) o x/(1-x^4) o x/(1-x^5) o x/(1-x^6) =
x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 17*x^6 + 35*x^7 + 73*x^8 + 152*x^9 +...
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{a(n)=local(A=x+x*O(x^n));if(n<=0,0,for(i=1,n,A=A/(1-A^(n-i+1)));polcoeff(A,n))}
for(n=1,30,print1(a(n),", "))
A136752
G.f.: A(x) = x/(1-x) o x/(1-x^2) o x/(1-x^4) o x/(1-x^8) o..., composition of functions x/(1 - x^{2^n}) for n=0,1,2,3,...
Original entry on oeis.org
1, 1, 2, 3, 6, 10, 19, 33, 61, 108, 198, 354, 645, 1159, 2106, 3795, 6874, 12405, 22457, 40560, 73374, 132578, 239782, 433362, 783602, 1416401, 2560953, 4629393, 8369741, 15130440, 27354520, 49451349, 89401972, 161622356, 292191262
Offset: 0
G.f.: A(x) is the limit of composition of functions x/(1-x^{2^n}):
F_0(x) = x/(1-x)
F_1(x) = F_1(x/(1-x^2)) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8*x^6 + 13x^7 +...
F_2(x) = F_2(x/(1-x^4)) = x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 +...
F_3(x) = x/(1-x) o x/(1-x^2) o x/(1-x^4) o x/(1-x^8) =
x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 + 33x^8 + 61x^9 + 108x^10 +...
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{a(n)=local(A=x+x*O(x^n));if(n<=0,0,m=#binary(n+1); for(i=1,m,A=A/(1-A^(2^(m-i))));polcoeff(A,n))}
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