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Search: id:A138519
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| A138519 |
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Expansion of q * (psi(q^5) / psi(q))^2 in powers of q where psi() is a Ramanujan theta function. |
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+0
5
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| 1, -2, 3, -6, 11, -16, 24, -38, 57, -82, 117, -168, 238, -328, 448, -614, 834, -1114, 1480, -1966, 2592, -3384, 4398, -5704, 7361, -9436, 12045, -15344, 19470, -24576, 30922, -38822, 48576, -60548, 75259, -93342, 115454, -142360, 175104, -214958, 263262, -321584, 391993
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Expansion of ((eta(q^10) / eta(q^2))^2 * eta(q) / eta(q^5))^2 in powers of q.
Euler transform of period 10 sequence [ -2, 2, -2, 2, 0, 2, -2, 2, -2, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u - v)^2 - v * (1 - u) * (1 - 5*u).
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u - v)^4 - u * (1 - u) * (1 - 5*u) * v * (1 - v) * (1 - 5*v).
G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = (1/5) g(t) where q = exp(2 pi i t) and g() is g.f. for A138518.
G.f.: x * (Product_{k>0} P(5,x^k) * P(10,x^k)^2)^2 where P(n,x) is the nth cyclotomic polynomial.
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EXAMPLE
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q - 2*q^2 + 3*q^3 - 6*q^4 + 11*q^5 - 16*q^6 + 24*q^7 - 38*q^8 + 57*q^9 + ...
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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 + A) / eta(x^5 + A) * ( eta(x^10 + A) / eta(x^2 + A) )^2)^2, n))}
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CROSSREFS
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A138520(n) = -a(n) unless n=0. A138521(n) = -5 * a(n) unless n=0. Convolution inverse of A138516.
Sequence in context: A076307 A102990 A138520 this_sequence A049794 A121617 A157656
Adjacent sequences: A138516 A138517 A138518 this_sequence A138520 A138521 A138522
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 23 2008
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