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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,...
6
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
0,3
COMMENTS
The composition transpose of A136750.
EXAMPLE
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 + ...
PROG
(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))}
for(n=1, 40, print1(a(n), ", "))
CROSSREFS
Cf. A064580. - Gary W. Adamson, Jun 21 2009
Sequence in context: A036765 A246555 A366023 * A154836 A087626 A125094
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 21 2008
STATUS
approved