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A101055
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E.g.f.: exp(exp(x)-1)/(1-x)^3.
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2
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1, 4, 20, 119, 819, 6397, 55919, 541144, 5746596, 66475311, 832418065, 11222752125, 162133146877, 2499401777680, 40960858008040, 711240364356155, 13045720176453587, 252079975222183461, 5118581045978055067, 108972887981432267708, 2427417968714846394712, 56467770394205361146187
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OFFSET
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0,2
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COMMENTS
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Sequence appears in the problem of normal ordering of functions of boson operators.
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LINKS
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FORMULA
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a(n) = ((-1)^n*n!/e)*Sum_{k>=0} L(n,-n-3,k)/k!, where L is a generalized Laguerre polynomial.
a(n) = (1/2)*Sum_{k=0..n} binomial(n,k)*(k + 2)!*Bell(n-k), where Bell() = A000110. - Ilya Gutkovskiy, May 24 2018
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Exp[Exp[x]-1]/(1-x)^3, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 11 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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