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Search: id:A123653
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| A123653 |
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Expansion of (eta(q^2)eta(q^6)/(eta(q)eta(q^3)))^6 in powers of q. |
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+0
2
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| 1, 6, 21, 68, 198, 510, 1248, 2904, 6393, 13604, 28044, 55956, 108982, 207552, 386622, 707216, 1271970, 2250582, 3925780, 6757272, 11483232, 19290824, 32057352, 52722744, 85884503, 138644292, 221885805, 352241792, 554892894
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Expansion of q/(chi(-q)*chi(-q^3))^6 in powers of q where chi() is a Ramanujan theta function.
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FORMULA
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Euler transform of period 6 sequence [ 6, 0, 12, 0, 6, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= u^2 -v*(1+12*u+64*u*v)
G.f.: x*(Product_{k>0} (1+x^k)*(1+x^(3k)))^6.
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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+A)/eta(x^3+A))^6, n))}
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CROSSREFS
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Adjacent sequences: A123650 A123651 A123652 this_sequence A123654 A123655 A123656
Sequence in context: A134931 A119103 A107653 this_sequence A101904 A022814 A000390
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Oct 04 2006
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