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Search: id:A109506
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| A109506 |
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Expansion of (1-eta(q)^8/et(q^2)^4)/8 in powers of q. |
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+0
3
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| 1, -3, 4, -3, 6, -12, 8, -3, 13, -18, 12, -12, 14, -24, 24, -3, 18, -39, 20, -18, 32, -36, 24, -12, 31, -42, 40, -24, 30, -72, 32, -3, 48, -54, 48, -39, 38, -60, 56, -18, 42, -96, 44, -36, 78, -72, 48, -12, 57, -93, 72, -42, 54, -120, 72, -24, 80, -90, 60, -72, 62, -96, 104, -3, 84, -144, 68, -54, 96, -144, 72
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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G. Chrystal, Algebra: An elementary text-book for the higher classes of secondary schools and for colleges, 6th ed, Chelsea Publishing Co., New York 1959 Part II, p. 346 Exercise XXI(18). MR0121327 (22 #12066)
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FORMULA
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a(n) = Sum_{d divides n} (-1)^(n/d+d)*d.
Multiplicative with a(2^e) = -3, if e>0. a(p^e) = (p^(e+1)-1)/(p-1) if p>2.
G.f.: Sum_{k>0} k(x^k/(1-x^k) -6x^(2k)/(1-x^(2k)) +8x^(4k)/(1-x^(4k))).
G.f.: Sum_{k>0} -(-x)^k/(1+x^k)^2 = Sum_{k>0} -k*(-x)^k/(1+x^k).
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PROGRAM
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(PARI) a(n)=if(n<1, 0, -(-1)^n*sumdiv(n, d, if(d%4, d)))
(PARI) {a(n)=local(A); if(n<1, 0, A=x*O(x^n); -1/8*polcoeff( eta(x+A)^8/eta(x^2+A)^4, n))}
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CROSSREFS
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a(n)=-(-1)^n*A046897(n). a(n)=-A096727(n)/8, if n>0.
Sequence in context: A048250 A073181 A046897 this_sequence A000113 A069915 A033634
Adjacent sequences: A109503 A109504 A109505 this_sequence A109507 A109508 A109509
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Jun 30 2005
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