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A169976
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Expansion of (psi(x)^24 + psi(-x)^24) / 2 in powers of x^2 where psi() is a Ramanujan theta function.
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1
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1, 276, 11178, 177400, 1612875, 10131156, 48897678, 193740408, 658523925, 1980143600, 5386270686, 13477895856, 31425764410, 68969957700, 143635113000, 285718115112, 545796171084, 1005775268868, 1794713445350, 3111031518000
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = (A013959(2*n + 3) - A000594(2*n + 3)) / 176896 = A014809(2*n).
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EXAMPLE
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1 + 276*x + 11178*x^2 + 177400*x^3 + 1612875*x^4 + 10131156*x^5 + ...
q^3 + 276*q^5 + 11178*q^7 + 177400*q^9 + 1612875*q^11 + 10131156*q^13 + ...
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MATHEMATICA
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QP:= Pochhammer; a[n_]:= SeriesCoefficient[(QP[q, q])^24*(QP[-q^(1/2), q^(1/2)]^24 + QP[q^(1/2), -q^(1/2)]^24)/2, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Apr 04 2018 *)
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, n *= 2; A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 / eta(x + A))^24, n))}
(PARI) {a(n) = if( n<0, 0, n = 2*n + 3; (sigma(n, 11) - polcoeff( x * eta(x + x * O(x^n))^24, n)) / 176896 )}
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CROSSREFS
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Sequence in context: A107080 A333049 A297525 * A297755 A166192 A186466
Adjacent sequences: A169973 A169974 A169975 * A169977 A169978 A169979
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 15 2010
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STATUS
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approved
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