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A080964
Euler transform of period-16 sequence [2,-3,2,1,2,-3,2,-6,2,-3,2,1,2,-3,2,-3,...].
3
1, 2, 0, 0, 4, 4, 0, 0, 2, -2, 0, 0, -8, -4, 0, 0, -4, 0, 0, 0, 8, -8, 0, 0, -8, -2, 0, 0, -16, 4, 0, 0, 6, -8, 0, 0, 12, 4, 0, 0, 8, 8, 0, 0, -8, 4, 0, 0, -8, 2, 0, 0, 24, -4, 0, 0, 0, 8, 0, 0, -16, 4, 0, 0, 12, 8, 0, 0, 16, 0, 0, 0, 10, -8, 0, 0, -24, 0, 0, 0, -8, -6, 0, 0, 16, 8, 0, 0, -24, -8, 0, 0, -16, -8, 0, 0, 8, 0, 0
OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..20000 (1501 terms from G. C. Greubel)
FORMULA
a(4*n+2) = a(4*n+3) = 0.
a(n) = 2*A072071(n) - A072070(n).
a(4*n) = A080965(n).
a(4*n+1) = 2*A080966(n).
Expansion of eta(q^2)^5*eta(q^8)^7/(eta(q)^2*eta(q^4)^4*eta(q^16)^3) in powers of q. - G. C. Greubel, Jul 02 2018
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[eta[q^2]^5 *eta[q^8]^7/(eta[q]^2*eta[q^4]^4*eta[q^16]^3), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 70}] (* G. C. Greubel, Jul 02 2018 *)
PROG
(PARI) a(n)=local(X); if(n<0, 0, X=x+x*O(x^n); polcoeff(eta(X)^-2*eta(X^2)^5*eta(X^4)^-4*eta(X^8)^7*eta(X^16)^-3, n))
CROSSREFS
Sequence in context: A072740 A226288 A185146 * A367054 A134014 A004531
KEYWORD
sign
AUTHOR
Michael Somos, Feb 28 2003
STATUS
approved