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Search: id:A022569
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| A022569 |
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Expansion of Product (1+q^m)^4; m=1..inf. |
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+0
2
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| 1, 4, 10, 24, 51, 100, 190, 344, 601, 1024, 1702, 2768, 4422, 6948, 10752, 16424, 24782, 36972, 54602, 79872, 115805, 166540, 237664, 336720, 473856, 662596, 920934, 1272728, 1749407, 2392268, 3255410, 4409344, 5945730, 7983388
(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 chi(-q)^(-4) in powers of q where chi() is a Ramanujan theta function.
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FORMULA
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Expansion of q^(-1/6) * (eta(q^2) / eta(q))^4 in powers of q.
Euler transform of period 2 sequence [ 4, 0, ...]. - Michael Somos Apr 26 2008
Given G.f. A(x) then B(x) = (A(x^6) * x)^2 satisfies 0 = f(B(x), B(x^2)) where f(u, v) = v * (1 + 16 * u * v) - u^2. - Michael Somos Apr 26 2008
Given G.f. A(x) then B(x) = A(x^6) * x satisfies 0 = f(B(x), B(x^2), B(x^4)) where f(u, v, w) = v * (u^2 - v) - 4 * w^2 * (u^2 + v). - Michael Somos Apr 26 2008
G.f. is a period 1 Fourier series which satisfies f(-1/(72 t)) = (1/4) / f(t) where q = exp(2 pi i t).
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EXAMPLE
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q + 4*q^7 + 10*q^13 + 24*q^19 + 51*q^25 + 100*q^31 + 190*q^37 + 344*q^43 + ...
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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) / eta(x + A))^4, n))} /* Michael Somos Apr 26 2008 */
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CROSSREFS
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Convolution inverse of A022599.
Adjacent sequences: A022566 A022567 A022568 this_sequence A022570 A022571 A022572
Sequence in context: A058514 A001979 A128516 this_sequence A093831 A052365 A107659
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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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