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Search: id:A113186
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| A113186 |
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Expansion of (25phi(q)phi^3(q^5)-phi^5(q)/phi(q^5)-24)/40 in powers of q where phi(q) is a Ramanujan theta function. |
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+0
1
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| 1, -1, -2, -1, 1, 2, -6, -1, 7, -1, 12, 2, -12, 6, -2, -1, -16, -7, 20, -1, 12, -12, -22, 2, 1, 12, -20, 6, 30, 2, 32, -1, -24, 16, -6, -7, -36, -20, 24, -1, 42, -12, -42, -12, 7, 22, -46, 2, 43, -1, 32, 12, -52, 20, 12, 6, -40, -30, 60, 2, 62, -32, -42, -1, -12, 24, -66, 16, 44, 6, 72, -7, -72, 36, -2, -20, -72, -24, 80, -1
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 249 Entry 8(iii).
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FORMULA
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a(n) is multiplicative with a(2^e) = -1 if e>0, a(5^e) = 1, a(p^e) = (p^(e+1)-1)/(p-1) if p == 1, 9 (mod 10), a(p^e) = ((-p)^(e+1)-1)/(-p-1) if p == 3, 7 (mod 10).
G.f.: (25phi(q) phi(q^5)^3 - phi(q)^5/phi(q^5)-24)/40 where phi(q)=1+2(q+q^4+q^9+...).
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PROGRAM
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(PARI) a(n)=if(n<1, 0, (-1)^n*sumdiv(n, d, kronecker(20, d)*d*(-1)^d))
(PARI) {a(n)=local(A, p, e); if(n<1, n==0, A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2, -1, if(p==5, 1, p*=kronecker(5, p); (p^(e+1)-1)/(p-1))))))}
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CROSSREFS
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Sequence in context: A025242 A163982 A156588 this_sequence A123218 A007736 A107042
Adjacent sequences: A113183 A113184 A113185 this_sequence A113187 A113188 A113189
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Oct 17 2005
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