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A058559
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McKay-Thompson series of class 20d for Monster.
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3
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1, 0, 3, -4, 4, -4, 7, -12, 13, -16, 22, -28, 38, -44, 55, -72, 83, -104, 129, -156, 187, -220, 273, -328, 384, -452, 539, -652, 757, -880, 1041, -1220, 1428, -1652, 1924, -2244, 2585, -2992, 3458, -3992, 4581, -5244, 6053, -6936, 7910, -9024, 10303, -11784, 13380, -15176, 17257, -19584
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history;
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OFFSET
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-1,3
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LINKS
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FORMULA
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Expansion of sqrt( 4 + (eta(q)*eta(q^5)/(eta(q^2)*eta(q^10)))^4 ) in powers of q. - G. C. Greubel, Jun 14 2018
a(n) ~ -(-1)^n * exp(sqrt(2*n/5)*Pi) / (2^(5/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T20d = 1/q + 3*q^3 - 4*q^5 + 4*q^7 - 4*q^9 + 7*q^11 - 12*q^13 + 13*q^15 - ...
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MATHEMATICA
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QP = QPochhammer; A = (QP[q]*(QP[q^5]/QP[q^2]/QP[q^10]))^4 + 4*q + O[q]^40;
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PROG
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(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff(sqrtn( (eta(x + A) * eta(x^5 + A) / eta(x^2 + A) / eta(x^10 + A))^4 + 4 * x, 2), n))} /* Georg Fischer, Nov 15 2020 [adapted from Michael Somos' PARI in A058098] */
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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