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Search: id:A128643
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| A128643 |
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Expansion of (b(q^2)/ b(q))^3 in powers of q where b() is a cubic AGM analog function. |
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3
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| 1, 9, 45, 171, 549, 1566, 4095, 10008, 23157, 51201, 108918, 224100, 447831, 872118, 1659672, 3093498, 5658453, 10173762, 18006021, 31408092, 54053190, 91869192, 154331028, 256447080, 421789671, 687086127, 1109128014, 1775103507
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of (chi(-q^2)/ chi(-q)^3)^3 in powers of q where chi() is a Ramanujan theta function.
Expansion of ((eta(q^2)/ eta(q))^3* (eta(q^3)/ eta(q^6)))^3 in powers of q.
Euler transform of period 6 sequence [ 9, 0, 6, 0, 9, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v* (1-v)* (1+8*u) +(u-v)^2.
G.f.: (Product_{k>0} (1+x^k)/ (1+x^(3k))^3)^3
G.f. is a period 1 Fourier series which satisfies f(-1 / (6 t)) = (1 / 8) g(t) where q = exp(2 pi i t) and g() is g.f. for A105559.
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EXAMPLE
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1 + 9*q + 45*q^2 + 171*q^3 + 549*q^4 + 1566*q^5 + 4095*q^6 + 10008*q^7 + ...
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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^2+A)/ eta(x+A))^3* eta(x^3+A)/ eta(x^6+A))^3, n))}
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CROSSREFS
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9*A128638(n) = a(n) unless n = 0. Convolution inverse of A128642.
Sequence in context: A145458 A145137 A144902 this_sequence A036826 A022574 A050574
Adjacent sequences: A128640 A128641 A128642 this_sequence A128644 A128645 A128646
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 16 2007
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