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 A058578 McKay-Thompson series of class 24H for Monster. 3
 1, 2, 5, 8, 14, 22, 34, 52, 75, 108, 152, 212, 293, 398, 539, 720, 956, 1260, 1646, 2140, 2761, 3548, 4532, 5760, 7292, 9186, 11532, 14416, 17958, 22292, 27576, 34012, 41815, 51264, 62672, 76416, 92941, 112756, 136481, 164816, 198602, 238810 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994). FORMULA Given g.f. A(x), then B(x)=A(x^2)^2/x^2 satisfies 0=f(B(x), B(x^2)) where f(u, v)= -uv(1+u^2v^2) +7uv(u+v)(1+uv) +9uv(u^2+v^2). - Michael Somos, May 16 2004 Expansion of q^(1/2)(eta(q^3)eta(q^4)/(eta(q)eta(q^12)))^2 in powers of q. - Michael Somos, May 16 2004 Euler transform of period 12 sequence [2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, ...]. - Michael Somos, May 16 2004 a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(5/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 10 2015 EXAMPLE T24H = 1/q + 2*q + 5*q^3 + 8*q^5 + 14*q^7 + 22*q^9 + 34*q^11 + 52*q^13 + ... MATHEMATICA nmax = 50; CoefficientList[Series[Product[((1-x^(3*k)) * (1-x^(4*k)) / ((1-x^k) * (1-x^(12*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 10 2015 *) PROG (PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff((eta(x^3+A)*eta(x^4+A)/eta(x+A)/eta(x^12+A))^2, n)) /* Michael Somos, May 16 2004 */ CROSSREFS Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc. Sequence in context: A182377 A327380 A330378 * A261526 A295392 A023674 Adjacent sequences:  A058575 A058576 A058577 * A058579 A058580 A058581 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 27 2000 STATUS approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)