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Search: id:A058706
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| A058706 |
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McKay-Thompson series of class 52B for Monster. |
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+0
1
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| 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; listen)
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OFFSET
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0,4
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REFERENCES
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D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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FORMULA
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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))).
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EXAMPLE
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T52B = 1/q + q + q^3 + 2*q^5 + 2*q^7 + 3*q^9 + 4*q^11 + 5*q^13 + 6*q^15 + ...
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PROGRAM
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(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 */
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Adjacent sequences: A058703 A058704 A058705 this_sequence A058707 A058708 A058709
Sequence in context: A034142 A008675 A027581 this_sequence A034143 A034144 A034145
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KEYWORD
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nonn
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AUTHOR
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njas, Nov 27, 2000
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