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A277378
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Expansion of e.g.f. exp(2*x/(1-x))/sqrt(1-x^2).
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2
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1, 2, 9, 50, 361, 3042, 29929, 331298, 4100625, 55777922, 828691369, 13316140818, 230256982201, 4257449540450, 83834039024649, 1750225301567618, 38614608429012001, 897325298084953602, 21904718673762721225, 560258287738117292018, 14981472258320814527241
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: exp(2*x/(1-x))/sqrt(1-x^2).
a(n) = |H_n(i)|^2 / 2^n = H_n(i) * H_n(-i) / 2^n, where H_n(x) is n-th Hermite polynomial, i = sqrt(-1).
D-finite with recurrence: (n+2)*(a(n) + n*a(n-1)) = a(n+1) + n*(n-1)^2*a(n-2).
a(n) ~ n^n / (2 * exp(1 - 2*sqrt(2*n) + n)) * (1 + 2*sqrt(2)/(3*sqrt(n))). - Vaclav Kotesovec, Oct 27 2021
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MATHEMATICA
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Table[Abs[HermiteH[n, I]]^2/2^n, {n, 0, 20}]
With[{nn=20}, CoefficientList[Series[Exp[2x/(1-x)]/Sqrt[1-x^2], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jan 27 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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