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A283334 G.f.: 1/(1 - x*d/dx log(eta(x))), where eta(x) is Dedekind's eta(q) function without the q^(1/24) factor. 2
1, -1, -2, 1, 2, 4, -6, -5, 4, 1, 18, -13, -26, 4, 22, 66, -76, -78, 66, 37, 122, -136, -144, 10, 54, 599, -368, -746, 196, 568, 744, -938, -156, -312, -1428, 2720, 3340, -2324, -8588, 1520, 8814, 4846, 1380, -16565, -16966, -6324, 79170, 47250, -160346 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Bernhard Heim, Markus Neuhauser, and Robert Troeger, Zeros Transfer For Recursively defined Polynomials, arXiv:2304.02694 [math.NT], 2023. See Table 5 p. 14.
FORMULA
a(n) = -Sum_{k=0..n-1} sigma(n-k)*a(k) for n>0 with a(0) = 1.
G.f.: 1/(1 + Sum_{k>=1} k*x^k/(1 - x^k)). - Ilya Gutkovskiy, Oct 18 2018
EXAMPLE
G.f.: A(x) = 1 - x - 2*x^2 + x^3 + 2*x^4 + 4*x^5 - 6*x^6 - 5*x^7 + ...
1/A(x) = 1 - x*d/dx log(eta(x)) = 1 + x + 3*x^2 + 4*x^3 + 7*x^4 + ... + sigma(n)*x^n + ...
eta(x)^3/A(x) = 1 - 2*x + 7*x^6 - 21*x^10 + 44*x^15 - 78*x^21 + ... + A184366(n)*x^n + ...
PROG
(PARI) lista(nn) = {va = vector(nn); va[1] = 1; for (n=1, nn-1, va[n+1] = -sum(k=0, n-1, sigma(n-k)*va[k+1]); ); va; } \\ Michel Marcus, Mar 05 2017
CROSSREFS
Cf. A180305 (1/(1 + x*d/dx log(eta(x)))), A184366.
Sequence in context: A324225 A214739 A296159 * A301413 A305056 A112179
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 05 2017
STATUS
approved

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Last modified March 19 07:41 EDT 2024. Contains 370958 sequences. (Running on oeis4.)