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Search: id:A123632
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| A123632 |
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Expansion of q / (chi(-q) * chi(-q^3) * chi(-q^5) * chi(-q^15)) in powers of q where chi() is a Ramanujan theta function. |
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2
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| 1, 1, 1, 3, 3, 5, 8, 9, 13, 19, 24, 31, 42, 52, 67, 91, 110, 137, 180, 217, 272, 344, 412, 509, 633, 762, 925, 1132, 1354, 1631, 1984, 2353, 2808, 3382, 3992, 4747, 5658, 6644, 7850, 9291, 10882, 12772, 15016, 17512, 20455, 23944, 27796, 32311, 37633, 43529
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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Euler transform of period 30 sequence [ 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= u^2 -v -u*v*(2 + 4*v).
Expansion of (eta(q^2) * eta(q^6) * eta(q^10) * eta(q^30)) / (eta(q) * eta(q^3) * eta(q^5) * eta(q^15)) in powers of q.
G.f. is a Fourier series which satisfies f(-1 / (30 t)) = (1/4) / f(t) where q = exp(2 pi i t).
G.f.: x * Product_{k>0} (1 + x^k) * (1 + x^(3*k)) * (1 + x^(5*k)) * (1 + x^(15*k)).
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EXAMPLE
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q + q^2 + q^3 + 3*q^4 + 3*q^5 + 5*q^6 + 8*q^7 + 9*q^8 + 13*q^9 + 19*q^10 + ...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^6+A)*eta(x^10+A)*eta(x^30+A)/ (eta(x+A)*eta(x^3+A)*eta(x^5+A)*eta(x^15+A)), n))}
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CROSSREFS
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Convolution inverse of A132321.
Sequence in context: A147095 A161626 A105888 this_sequence A039868 A015723 A116645
Adjacent sequences: A123629 A123630 A123631 this_sequence A123633 A123634 A123635
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Oct 03 2006, Jan 12 2009
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