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A119952
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Expansion of psi(-q^7)psi(-q^9)/(q^6*psi(-q)psi(-q^63)).
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0
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1, 1, 1, 2, 3, 4, 5, 6, 9, 11, 13, 17, 22, 27, 32, 40, 51, 61, 72, 88, 108, 128, 150, 180, 217, 255, 297, 351, 416, 485, 562, 657, 770, 891, 1026, 1190, 1380, 1587, 1818, 2092, 2409, 2754, 3139, 3590, 4105, 4670, 5299, 6026, 6854, 7761, 8770, 9926, 11231
(list; graph; refs; listen; history; internal format)
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OFFSET
| -6,4
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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).
psi(q) = Sum_{k>0} q^((k^2+k)/2) is a Ramanujan theta function.
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REFERENCES
| B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 426 Entry 19(ii).
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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
| Euler transform of period 252 {0,1} sequence.
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EXAMPLE
| q^-6 +q^-5 +q^-4 +2*q^-3 +3*q^-2 +4*q^-1 +5 +6*q +9*q^2 +...
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PROG
| (PARI) {a(n)=local(A); if(n<-6, 0, n+=6; A=sum(k=0, (sqrtint(8*n+1)-1)\2, (-x)^((k^2+k)/2), x*O(x^n)); polcoeff( subst(A+x*O(x^(n\7)), x, x^7) *subst(A+x*O(x^(n\7)), x, x^9) /A /subst(A+x*O(x^(n\63)), x, x^63), n))}
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CROSSREFS
| Sequence in context: A080112 A123924 A036023 * A102571 A064278 A125155
Adjacent sequences: A119949 A119950 A119951 * A119953 A119954 A119955
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, May 30 2006
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