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A247480
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G.f. A(x) satisfies: x = Sum_{n>=1} 1/A(x)^(5*n) * Product_{k=1..n} (1 - 1/A(x)^(2*k-1)).
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3
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1, 1, 3, 21, 172, 1557, 14937, 148870, 1523150, 15874211, 167584946, 1784250269, 19082848084, 204183773733, 2174724531143, 22887441573480, 235016048710027, 2294441979279215, 19936497820248076, 118333942636382173, -709004900481995789, -49850788347995316262
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ c * 12^n * n^(n-2) / (exp(n) * Pi^(2*n)), where c = -sqrt(6) * Pi^3 * exp(5*Pi^2/24)/24 = -24.7341070998048267... - Vaclav Kotesovec, Dec 01 2014, updated Aug 22 2017
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MATHEMATICA
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nmax = 20; aa = ConstantArray[0, nmax]; aa[[1]] = 1; Do[AGF = 1+Sum[aa[[n]]*x^n, {n, 1, j-1}]+koef*x^j; sol=Solve[SeriesCoefficient[Sum[Product[(1-1/AGF^(2m-1))/AGF^5, {m, 1, k}], {k, 1, j}], {x, 0, j}]==0, koef][[1]]; aa[[j]]=koef/.sol[[1]], {j, 2, nmax}]; Flatten[{1, aa}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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