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Search: id:A128517
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| A128517 |
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Expansion of q^(-1)* (chi(-q^9)/ chi(-q))^3 in powers of q where chi() is a Ramanujan theta function. |
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+0
1
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| 1, 3, 6, 13, 24, 42, 73, 120, 192, 299, 456, 684, 1007, 1464, 2100, 2976, 4176, 5802, 7993, 10920, 14808, 19946, 26688, 35496, 46944, 61752, 80826, 105286, 136536, 176304, 226725, 290448, 370704, 471467, 597600, 755028, 950980, 1194216
(list; graph; listen)
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OFFSET
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-1,2
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FORMULA
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Expansion of (eta(q^2)* eta(q^9)/ (eta(q)* eta(q^18)))^3 in powers of q.
Euler transform of period 18 sequence [ 3, 0, 3, 0, 3, 0, 3, 0, 0, 0, 3, 0, 3, 0, 3, 0, 3, 0, ...].
G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= (u^2-v)* (w^2-v) -u*w* (6*(1+v^2) -10*v).
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (u*v -u-v)^3 -u*v* (u+v-1)^3.
G.f. is Fourier series of a level 18 modular function. f(-1/(18t))= f(t) where q= exp(2 pi i t).
G.f.: (1/x)* (Product_{k>0} P(x^k))^-3 where P(x)= (x^2 -x +1)* (x^6 -x^3 +1).
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EXAMPLE
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1/q + 3 + 6*q + 13*q^2 + 24*q^3 + 42*q^4 + 73*q^5 + 120*q^6 + ...
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PROGRAM
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(PARI) {a(n)= if(n<-1, 0, n++; A=x*O(x^n); polcoeff( (eta(x^2+A)* eta(x^9+A)/ (eta(x+A)* eta(x^18+A)))^3, n))}
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CROSSREFS
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A058535(n)=a(n) if n nonzero.
Sequence in context: A002799 A162426 A058554 this_sequence A022568 A120006 A061567
Adjacent sequences: A128514 A128515 A128516 this_sequence A128518 A128519 A128520
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 06 2007
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