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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The composition transpose of A136750.

LINKS

Table of n, a(n) for n=0..26.

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. A136750; variants: A136752, A136753, A119470, A119471.

Cf. A064580. - Gary W. Adamson, Jun 21 2009

Sequence in context: A339290 A036765 A246555 * A154836 A087626 A125094

Adjacent sequences:  A136748 A136749 A136750 * A136752 A136753 A136754

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 21 2008

STATUS

approved

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Last modified May 20 03:37 EDT 2022. Contains 353851 sequences. (Running on oeis4.)