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Search: id:A128525
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| A128525 |
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McKay-Thompson series of class 11A for the Monster Group with a(0) = 6. |
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2
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| 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; listen)
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OFFSET
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-1,2
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LINKS
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Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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G.f. is Fourier series of a level 11 modular function. f(-1/(11t))= f(t) where q= exp(2 pi i t).
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.
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.
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EXAMPLE
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1/q + 6 + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ...
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PROGRAM
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(PARI) {a(n)= local(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))}
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CROSSREFS
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A058205(n)=a(n) if n nonzero.
Sequence in context: A048746 A026382 A054492 this_sequence A083334 A088016 A010330
Adjacent sequences: A128522 A128523 A128524 this_sequence A128526 A128527 A128528
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 07 2007
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