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A058706 McKay-Thompson series of class 52B for Monster. 1
1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 21, 26, 30, 36, 43, 50, 59, 70, 81, 94, 110, 127, 147, 170, 195, 224, 258, 294, 336, 384, 436, 496, 564, 638, 722, 816, 920, 1037, 1168, 1312, 1473, 1654, 1851, 2072, 2317, 2586, 2886, 3218, 3583, 3986, 4432, 4922, 5462 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1500

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of q*eta(q^4)eta(q^26)/(eta(q^2)eta(q^52)) in powers of q^2. - Michael Somos, May 03 2005

Euler transform of period 26 sequence [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, ...]. - Michael Somos, May 03 2005

Given g.f. A(x), then B(x)=(A(x^2)/x)^2 satisfies 0=f(B(x), B(x^2)) where f(u, v)= u^3 +v^3 -u^3*v^3 -6*u^2*v^2 -u*v +4*u^3*v^2 +4*u^2*v^3 -4*u^3*v -4*u*v^3 +4*u^2*v +4*u*v^2 +u^4*v +u*v^4. - Michael Somos, May 03 2005

Given g.f. A(x), then B(x)=A(x^2)/x satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u, v, w)= v^4 -v^3 -v^2 -u^2*v -w^2*v +u^2*w^2 +u^2*v^2 +w^2*v^2 +u^2*w^2*v +u^2*v^3 +w^2*v^3 -u^2*w^2*v^2. - Michael Somos, May 03 2005

Given g.f. A(x), then B(x)=A(x^2)/x satisfies 0=f(B(x), B(x^2), B(x^3), B(x^6)) where f(u1, u2, u3, u6)=u2^4 -u6^3*u2^3 +3*u6*u2^3 +3*u6^2*u2^2 +3*u6^3*u2 -u6*u2 +u6^4. - Michael Somos, May 03 2005

G.f. Product_{k>0} (1-x^(2k))(1-x^(13k))/((1-x^k)(1-x^(26k))).

a(n) ~ exp(2*Pi*sqrt(n/13)) / (2 * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 06 2015

EXAMPLE

T52B = 1/q + q + q^3 + 2*q^5 + 2*q^7 + 3*q^9 + 4*q^11 + 5*q^13 + 6*q^15 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1+x^k) / (1+x^(13*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 06 2015 *)

eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q^2]*eta[q^13]/(eta[q]*eta[q^26])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 27 2018 *)

PROG

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^13+A)/eta(x+A)/eta(x^26+A), n))} /* Michael Somos, May 03 2005 */

CROSSREFS

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

Sequence in context: A034142 A008675 A027581 * A034143 A309999 A034144

Adjacent sequences:  A058703 A058704 A058705 * A058707 A058708 A058709

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved

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Last modified October 15 00:04 EDT 2019. Contains 328025 sequences. (Running on oeis4.)