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Search: id:A128758
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| A128758 |
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Expansion of q^(-1/3)* (eta(q^3)/ eta(q))^4 in powers of q. |
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4
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| 1, 4, 14, 36, 89, 196, 416, 828, 1600, 2972, 5390, 9504, 16436, 27828, 46364, 75960, 122772, 195728, 308430, 480456, 740921, 1131364, 1712348, 2569500, 3825641, 5652872, 8294612, 12089016, 17508609, 25204428, 36076540, 51355368, 72725909
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OFFSET
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0,2
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FORMULA
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Expansion of q^(-1/3)* (1/3)* c(q)/ b(q) in powers of q where b(), c() are cubic AGM analog functions.
Euler transform of period 3 sequence [ 4, 4, 0, ...].
Given g.f. A(x), then B(x)= x*A(x^3) satisfies 0= f(B(x), B(x^2)) where f(u, v)= (u+v)^3 -u*v* (1+3*u)* (1+3*v).
Given g.f. A(x), then B(x)= x*A(x^3) satisfies 0= f(B(x), B(x^2), B(x^4)) where f(u, v, w)= u^2 +w^2 +u*w -v -9*v^2* (u+w).
G.f.: (Product_{k>0} (1 +x^k +x^(2k)) )^4.
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EXAMPLE
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q + 4*q^4 + 14*q^7 + 36*q^10 + 89*q^13 + 196*q^16 + 416*q^19 + ...
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PROGRAM
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(PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( (eta(x^3+A)/ eta(x+A))^4, n))}
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CROSSREFS
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A112146(3n+1)= 9* a(n).
Adjacent sequences: A128755 A128756 A128757 this_sequence A128759 A128760 A128761
Sequence in context: A079908 A038164 A034528 this_sequence A027166 A126943 A036368
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 24 2007
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