A058703 McKay-Thompson series of class 50a for Monster.

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

G. C. Greubel, Table of n, a(n) for n = -1..1000

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

Index entries for McKay-Thompson series for Monster simple group

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

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A288001 A034321 A034320 * A347588 A000009 A081360

Adjacent sequences: A058700 A058701 A058702 * A058704 A058705 A058706

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Joerg Arndt, Apr 09 2016

Status

approved