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A131964
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Expansion of phi(-q^4)* chi(-q^6)/ chi(-q) in powers of q where phi(), chi() are Ramanujan theta functions.
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4
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1, 1, 1, 2, 0, 1, 1, 0, 1, 0, 2, 1, 1, 1, 0, 1, 2, 2, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 2, 1, 1, 0, 1, 1, 1, 3, 0, 0, 0, 2, 1, 1, 2, 1, 2, 1, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 2, 1, 2, 1, 1, 1, 1, 0, 0, 0, 2, 1, 2, 0, 2, 2, 1, 1, 0, 0, 1, 3, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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).
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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
| Expansion of q^(-19/24)* eta(q^2)* eta(q^4)^2* eta(q^6)* eta(q^24)/( eta(q)* eta(q^8)* eta(q^12)) in powers of q.
Euler transform of period 24 sequence [ 1, 0, 1, -2, 1, -1, 1, -1, 1, 0, 1, -2, 1, 0, 1, -1, 1, -1, 1, -2, 1, 0, 1, -2, ...].
a(25n+19)= a(n). a(25n+4)= a(25n+9)= a(25n+14)= a(25n+24)= 0.
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PROG
| (PARI) {a(n)= if(n<0, 0, n=24*n+19; sumdiv(n, d, kronecker( -12, d)*(n/d %2))/2)}
(PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( eta(x^2+A)* eta(x^4+A)^2* eta(x^6+A)* eta(x^24+A)/ eta(x+A)/ eta(x^8+A)/ eta(x^12+A), n))}
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CROSSREFS
| Cf. A123484(24n+19)= 2*a(n).
Sequence in context: A025427 A091586 A116377 * A065339 A122434 A141571
Adjacent sequences: A131961 A131962 A131963 * A131965 A131966 A131967
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Aug 02 2007
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