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 A128525 McKay-Thompson series of class 11A for the Monster Group with a(0) = 6. 5
 1, 6, 17, 46, 116, 252, 533, 1034, 1961, 3540, 6253, 10654, 17897, 29284, 47265, 74868, 117158, 180608, 275562, 415300, 620210, 916860, 1344251, 1953974, 2819664, 4038300, 5746031, 8122072, 11413112, 15943576, 22153909, 30620666 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,2 LINKS G. C. Greubel, Table of n, a(n) for n = -1..1000 FORMULA Expansion of (1 + 3*F)^2 * (1/F + 1 + 3*F) where F = eta(q^3) * eta(q^33) / (eta(q) * eta(q^11)) in powers of q. G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 + v^2 - u^2*v^2 + 12*u*v*(u+v) - 20*(u^2+v^2) - 53*u*v + 56*(u+v) - 44. G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^4)) where f(u, v, w) = u^2 + w^2 + u*w - v^2*(u+w) + 12*v^2 + 12*v*(u+w) - 20*(u+w) - 53*v + 56. G.f. is a period 1 Fourier series which satisfies f(-1 / (11 t)) = f(t) where q = exp(2 Pi i t). a(n) = A058205(n) unless n = 0. Convolution of A028160 and A032442. - Michael Somos, Apr 21 2015 a(n) ~ exp(4*Pi*sqrt(n/11)) / (sqrt(2)*11^(1/4)*n^(3/4)). - Vaclav Kotesovec, Dec 04 2015 EXAMPLE G.f. = 1/q + 6 + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ With[{F = q QPochhammer[ q^3] QPochhammer[ q^33] / (QPochhammer[ q] QPochhammer[ q^11])}, (1 + 3 F)^2 (1/F + 1 + 3 F)], {q, 0, n}]; (* Michael Somos, Apr 21 2015 *) PROG (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = x * eta(x^3 + A) * eta(x^33 + A) / (eta(x + A) * eta(x^11 + A)); polcoeff( (1 + 3*A)^2 * (1/A + 1 + 3*A), n-1))}; CROSSREFS Cf. A028160, A032442, A058205, Sequence in context: A048746 A026382 A054492 * A083334 A199113 A297297 Adjacent sequences:  A128522 A128523 A128524 * A128526 A128527 A128528 KEYWORD nonn AUTHOR Michael Somos, Mar 07 2007 STATUS approved

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Last modified October 19 16:08 EDT 2019. Contains 328223 sequences. (Running on oeis4.)