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A124233
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Expansion of psi(q)*phi(-q^10)*chi(-q^5)/chi(-q^2) in powers of q where phi(),psi(),chi() are Ramanujan theta functions.
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1, 1, 1, 2, 1, 1, 2, 2, 1, 3, 1, 0, 2, 0, 2, 2, 1, 0, 3, 0, 1, 4, 0, 2, 2, 1, 0, 4, 2, 2, 2, 0, 1, 0, 0, 2, 3, 0, 0, 0, 1, 2, 4, 2, 0, 3, 2, 2, 2, 3, 1, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 2, 0, 6, 1, 0, 0, 2, 0, 4, 2, 0, 3, 0, 0, 2, 0, 0, 0, 0, 1, 5, 2, 2, 4, 0, 2, 4, 0, 2, 3, 0, 2, 0, 2, 0, 2, 0, 3, 0, 1, 2, 0, 2, 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
| Euler transform of period 20 sequence [ 1, 0, 1, -1, 0, 0, 1, -1, 1, -2, 1, -1, 1, 0, 0, -1, 1, 0, 1, -2, ...].
Moebius transform is period 20 sequence [ 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, ...].
Multiplicative with a(2^e) = a(5^e) = 1, a(p^e) = e+1 if p == 1, 3, 7, 9 (mod 20), a(p^e) = (1+(-1)^e)/2 if p == 11, 13, 17, 19 (mod 20).
Expansion of eta(q^2)*eta(q^4)*eta(q^5)*eta(q^10)/(eta(q)*eta(q^20)) in powers of q.
a(2n)=a(5n)=a(n), a(20n+11)=a(20n+13)=a(20n+17)=a(20n+19)=0.
G.f.: 1 +Sum_{k>0} x^k(1+x^(2k))(1+x^(6k))/(1+x^(10k)).
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PROG
| (PARI) {a(n)=if(n<1, n==0, sumdiv(n, d, kronecker(-20, d)))}
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^4+A)* eta(x^5+A)*eta(x^10+A)/ eta(x+A)/eta(x^20+A), n))}
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CROSSREFS
| Cf. A035170(n)=a(n) if n>0.
Sequence in context: A066888 A029313 A144001 * A035170 A111949 A143323
Adjacent sequences: A124230 A124231 A124232 * A124234 A124235 A124236
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KEYWORD
| nonn,mult
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AUTHOR
| Michael Somos, Oct 21 2006
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