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Search: id:A085140
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| A085140 |
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Expansion of q^(-1/6)eta(q^2)^3/eta(q)^2 in powers of q. |
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+0
2
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| 1, 2, 2, 4, 5, 6, 10, 12, 15, 20, 26, 32, 40, 50, 60, 76, 92, 110, 134, 160, 191, 230, 272, 320, 380, 446, 522, 612, 715, 830, 966, 1120, 1292, 1494, 1720, 1976, 2272, 2602, 2974, 3400, 3876, 4412, 5020, 5700, 6460, 7322, 8282, 9352, 10559, 11900, 13396
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Euler transform of period 2 sequence [2,-1,...].
In the notation of Dragonette generating function is G_2(q^(1/2))/2.
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REFERENCES
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L. A. Dragonette, Some asymptotic formulae for the Mock Theta Series of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500.
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FORMULA
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G.f.: Product_{k>0} (1-x^(2k))/(1-x^(2k-1))^2.
a(n) = b(n)+b(n-1)+b(n-3)+b(n-6)+...+b(n-k*(k+1)/2)+..., where b() is A000009(). E.g. a(8) = b(8)+b(7)+b(5)+b(2) = 6+5+3+1 = 15. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 18 2004
Expansion of psi(q)/chi(-q) = f(-q^2)/chi(-q)^2 = f(-q)/chi(-q)^3 = phi(-q)/chi(-q)^4 = phi(q)/chi(-q^2)^2 = f(-q^2)^2/phi(-q) = f(-q)^4/phi(-q)^3 = psi(q)^2/f(-q^2) = chi(q)^2*psi(q^2) = f(-q^2)^3/f(-q)^2 in powers of q where f(),phi(),psi(),chi() are Ramanujan theta functions. - Michael Somos Feb 18 2006
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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)^3/eta(x+A)^2, n))}
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CROSSREFS
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Adjacent sequences: A085137 A085138 A085139 this_sequence A085141 A085142 A085143
Sequence in context: A062436 A121269 A056219 this_sequence A138883 A107849 A053036
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jun 20, 2003
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