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A133738
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Expansion of product of 3rd order mock theta function phi(q) and Ramanujan theta function f(-q).
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1, 0, -2, -2, 2, 2, -2, 0, 2, 4, -2, -4, 2, 0, -2, -2, 2, 4, -4, -4, 2, 2, -2, 0, 4, 4, 0, -6, 2, 0, -2, 0, 2, 6, -4, -4, 4, 0, -4, -2, 0, 4, -2, -4, 2, 0, 0, 0, 4, 4, -2, -6, 2, 0, -6, 2, 2, 8, 0, -4, 2, 0, 0, 0, 2, 2, -6, -4, 2, 0, -2, 0, 4, 4, 0, -6, 2, -2, -2, 0, 0, 8, -4, -4, 2, -2, -4, 0, 2, 4, 0, -2, 2, 0, 0, 2, 4, 4, -2, -8, 2, 0, -6, 0, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| G.f.: 1 + 2 * Sum_{k>0} (-1)^k * x^(k*(3*k+1)/2) * (1 + x^k) / (1 + x^(2*k)).
G.f.: ( Product_{k>0} 1-x^k ) * ( 1 + Sum_{k>0} x^k^2 / ((1+x^2)(1+x^4)...(1+x^(2k))) ).
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PROG
| (PARI) {a(n) = if( n<0, 0, polcoeff( 1 + 2 * sum(k=1, (sqrtint(24*n+1) - 1) \ 6, (-1)^k * x^(k*(3*k+1)/2) * (1 + x^k) / (1 + x^(2*k)), x * O(x^n)), n))}
(PARI) {a(n) = local(t); if( n<0, 0, t = 1 + O(x^n); polcoeff( sum(k=1, sqrtint(n), t *= x^(2*k-1) / (1 + x^(2*k)) +O(x^(n-(k-1)^2+1)), 1) * eta(x + x*O(x^n)), n))}
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CROSSREFS
| Convolution of A053250 and A010815.
Sequence in context: A173069 A059963 A137934 * A111409 A125088 A027360
Adjacent sequences: A133735 A133736 A133737 * A133739 A133740 A133741
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Sep 22 2007
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