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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
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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; refs; listen; history; internal format)
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OFFSET
| -1,2
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| 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
| 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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PROG
| (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
| A058597(n)=a(n) if n nonzero.
Sequence in context: A194627 A173303 A058609 * A022567 A134004 A123631
Adjacent sequences: A128515 A128516 A128517 * A128519 A128520 A128521
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Mar 06 2007
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