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Search: id:A128518
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| A128518 |
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Expansion of q^(-1)* (chi(-q^13)/ chi(-q))^2 in powers of q where chi() is a Ramanujan theta function. |
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+0
1
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| 1, 2, 3, 6, 9, 14, 22, 32, 46, 66, 93, 128, 176, 236, 315, 420, 550, 718, 932, 1198, 1534, 1956, 2476, 3120, 3919, 4896, 6095, 7562, 9341, 11504, 14126, 17284, 21090, 25666, 31140, 37692, 45515, 54818, 65878, 79000, 94523, 112872, 134522, 160004
(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^13)/ (eta(q)* eta(q^26)))^2 in powers of q.
Euler transform of period 26 sequence [ 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 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* (4*(1+v^2) -4*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)* (u^2+v^2+1).
G.f. is Fourier series of a level 26 modular function. f(-1/(26t))= f(t) where q= exp(2 pi i t).
G.f.: (1/x)* (Product_{k>0} P(x^k))^-2 where P(x) is the 26th cyclotomic polynomial of degree 12.
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EXAMPLE
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1/q + 2 + 3*q + 6*q^2 + 9*q^3 + 14*q^4 + 22*q^5 + 32*q^6 + 46*q^7 + ...
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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^13+A)/ (eta(x+A)* eta(x^26+A)))^2, n))}
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CROSSREFS
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A058597(n)=a(n) if n nonzero.
Sequence in context: A094055 A094056 A058609 this_sequence A022567 A134004 A123631
Adjacent sequences: A128515 A128516 A128517 this_sequence A128519 A128520 A128521
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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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