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URL: https://oeis.org/A058703

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A058703
McKay-Thompson series of class 50a for Monster.
2
1, 0, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76, 89, 104, 122, 141, 164, 191, 220, 254, 293, 336, 385, 442, 504, 575, 656, 745, 846, 960, 1086, 1228, 1388, 1564, 1762, 1984, 2228, 2501, 2806, 3142, 3516, 3932, 4390, 4898, 5462, 6082, 6768, 7527, 8360, 9280, 10295, 11408, 12634, 13984, 15462
OFFSET
-1,4
COMMENTS
Apart from a(0) same as A034320. [Joerg Arndt, Apr 09 2016]
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014
FORMULA
G.f.: (E(q^2)*E(q^25))/(E(q)*E(q^50))/q - 1 where E(q) = prod(n>=1, 1 - q^n ). - Joerg Arndt, Apr 09 2016
a(n) ~ exp(2*Pi*sqrt(2*n)/5) / (2^(3/4) * sqrt(5) * n^(3/4)). - Vaclav Kotesovec, Sep 06 2017
EXAMPLE
T50a = 1/q + q + 2*q^2 + 2*q^3 + 3*q^4 + 4*q^5 + 5*q^6 + 6*q^7 + 8*q^8 + ...
MATHEMATICA
nmax = 60; CoefficientList[Series[-x + Product[(1 + x^k)/(1 + x^(25*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 06 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[-1 + (eta[q^2]*eta[q^25])/(eta[q]*eta[q^50]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018*)
PROG
(PARI) N=66; q='q+O('q^N); Vec( (eta(q^2)*eta(q^25))/(eta(q)*eta(q^50))/q - 1 ) \\ Joerg Arndt, Apr 09 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Joerg Arndt, Apr 09 2016
STATUS
approved