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Search: id:A136753
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| A136753 |
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G.f.: A(x) = ...o x/(1-x^8) o x/(1-x^4) o x/(1-x^2) o x/(1-x), composition of functions x/(1 - x^{2^n}) for n=...,3,2,1,0. |
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+0
4
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| 1, 1, 2, 4, 9, 21, 52, 134, 355, 955, 2590, 7052, 19246, 52638, 144368, 397468, 1099720, 3060936, 8577496, 24210808, 68843806, 197176726, 568585576, 1649739332, 4812731846, 14105205846, 41498665884, 122469937048
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The composition transpose of A136752.
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EXAMPLE
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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) = x/(1-x^2) o F_0(x) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 +...
F_2(x) = x/(1-x^4) o F_1(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...
F_3(x) = x/(1-x^8) o F_2(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...
F_4(x) = x/(1-x^16) o x/(1-x^8) o x/(1-x^4) o x/(1-x^2) o x/(1-x) =
x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 21*x^6 + 52*x^7 + 134*x^8 + 355*x^9 +...
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PROGRAM
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(PARI) {a(n)=local(A=x+x*O(x^n)); if(n<=0, 0, for(i=0, #binary(n+1), A=A/(1-A^(2^i))); polcoeff(A, n))}
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CROSSREFS
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Cf. A136752; variants: A136750, A136751, A119470, A119471.
Sequence in context: A001006 A027057 A000636 this_sequence A084261 A063026 A106219
Adjacent sequences: A136750 A136751 A136752 this_sequence A136754 A136755 A136756
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 21 2008
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