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Search: id:A029552
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| A029552 |
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Expansion of theta_3(2z)/eta(z). |
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3
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| 1, 3, 4, 7, 13, 19, 29, 43, 62, 90, 126, 174, 239, 325, 435, 580, 769, 1007, 1313, 1702, 2191, 2808, 3580, 4539, 5735, 7216, 9036, 11278, 14028, 17383, 21474, 26448, 32471, 39759, 48550, 59123, 71829, 87053, 105249, 126975, 152858, 183623
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Expansion of q^(1/24)eta(q^2)^5/(eta(q)^3 eta(q^4)^2) in powers of q. - Michael Somos Sep 17 2004
Euler transform of period 4 sequence [3,-2,3,0,...]. - Michael Somos, Sep 17 2004
G.f. A(x) is limit of x^(n^2)P_{2n}(1/x) where P_n(q) = Sum_{k=0..n} C(n,k;q) and C(n,k;q) is q-binomial coefficients. - Michael Somos, Sep 17 2004
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FORMULA
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G.f.: (1+2Sum_{k>0} x^(k^2))/(Product_{k>0} (1-x^k)).
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(sum(k=1, sqrtint(n), 2*x^k^2, 1)/eta(x+x*O(x^n)), n)) /* Michael Somos, Sep 17 2004 */
(PARI) a(n)= local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^5/(eta(x+A)^3*eta(x^4+A)^2), n)) /* Michael Somos, Sep 17 2004 */
(PARI) a(n)= if(n<0, 0, polcoeff( sum(k=0, 2*n, prod(i=1, k, (1-x^(2*n+1-i))/(1-x^i))), n^2-n)) /* Michael Somos, Sep 17 2004 */
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CROSSREFS
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Sequence in context: A093124 A055664 A089374 this_sequence A125118 A116201 A092406
Adjacent sequences: A029549 A029550 A029551 this_sequence A029553 A029554 A029555
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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