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A131961
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Expansion of q^(-1/24) * eta(q^3)^2 * eta(q^4)^5/( eta(q) * eta(q^2)* eta(q^6)* eta(q^8)^2) in powers of q.
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5
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1, 1, 3, 2, 2, 1, 0, 3, 2, 4, 2, 0, 1, 2, 2, 3, 0, 2, 2, 2, 4, 0, 1, 4, 2, 2, 1, 0, 2, 0, 4, 0, 2, 4, 4, 1, 0, 4, 0, 2, 3, 0, 2, 2, 4, 0, 0, 2, 2, 0, 2, 3, 2, 4, 2, 2, 0, 3, 4, 4, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 1, 0, 8, 2, 2, 2, 2, 3, 2, 4, 0, 0, 0, 2, 2, 4, 0, 2, 2, 2, 2, 0, 1, 0, 4, 2, 0, 0, 4, 2, 5, 2, 4, 2, 0
(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
| Expansion of phi(q^2)* phi(-q^3)/ chi(-q) in powers of q where phi(), chi() are Ramanujan theta functions.
Euler transform of period 24 sequence [ 1, 2, -1, -3, 1, 1, 1, -1, -1, 2, 1, -4, 1, 2, -1, -1, 1, 1, 1, -3, -1, 2, 1, -2, ...].
a(25n+1)= a(n). a(25n+6)= a(25n+11)= a(25n+16)= a(25n+21)= 0.
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PROG
| (PARI) {a(n)= if(n<0, 0, n=24*n+1; sumdiv(n, d, kronecker( -12, d)*(n/d %2)))}
(PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( eta(x^3+A)^2* eta(x^4+A)^5/ eta(x+A)/ eta(x^2+A)/ eta(x^6+A)/ eta(x^8+A)^2, n))}
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CROSSREFS
| Cf. A123484(24n+1)= a(n).
Sequence in context: A108335 A155917 A143378 * A010269 A077450 A086138
Adjacent sequences: A131958 A131959 A131960 * A131962 A131963 A131964
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Aug 02 2007
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