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Search: id:A132978
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| A132978 |
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Expansion of q^(-2/3) * (eta(q^2) * eta(q^6))^2 * eta(q^3) * eta(q^12) / ( eta(q)* eta(q^4) )^3 in powers of q. |
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1
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| 1, 3, 7, 15, 32, 63, 114, 201, 350, 591, 967, 1554, 2468, 3855, 5916, 8970, 13471, 20007, 29384, 42771, 61784, 88530, 125838, 177642, 249230, 347484, 481506, 663549, 909788, 1241127, 1684824, 2276781, 3063657, 4105275, 5478698, 7283709
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of q^(-2/3) * (psi(-q^3) / psi(-q)^3) * (c(q^2) / 3) in powers of q where psi() is a Ramanujan theta function and c() is a cubic AGM function.
Euler transform of period 12 sequence [ 3, 1, 2, 4, 3, -2, 3, 4, 2, 1, 3, 0, ...].
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EXAMPLE
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q^2 + 3*q^5 + 7*q^8 + 15*q^11 + 32*q^14 + 63*q^17 + 114*q^20 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A) * eta(x^6 + A)^2 * eta(x^12 + A) / ( eta(x + A) * eta(x^4 + A))^3, n))}
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CROSSREFS
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A132975(3*n+2) = a(n). Convolution of A132974 and A045833.
Sequence in context: A129984 A024876 A066175 this_sequence A117079 A026745 A139333
Adjacent sequences: A132975 A132976 A132977 this_sequence A132979 A132980 A132981
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Sep 07 2007
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