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A065980
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Inverse binomial transform of [1^1,2^2,3^3,...], shifted right by one index.
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1
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1, 3, 20, 186, 2248, 33340, 585744, 11891236, 273854368, 7053523236, 200894140120, 6268924259884, 212691682554960, 7795165961244532, 306908654169113416, 12918649608270463740, 578931362074039774144
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OFFSET
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1,2
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COMMENTS
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{0, a(n),n=1,...} = inverse binomial transform of {A001923(m), m=0,...} [From Tilman Neumann, Dec 17 2008]
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LINKS
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FORMULA
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O.g.f.: Sum_{n>0} (n*x/(1+x))^n. E.g.f.: int(-exp(-x)*LambertW(-x)/(1+LambertW(-x))^3/x, x). - Vladeta Jovovic, Apr 12 2003
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MATHEMATICA
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CoefficientList[Series[-E^(-x)*LambertW[-x]/(1+LambertW[-x])^3/x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 17 2014 *)
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PROG
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(PARI) a(n)=if(n<1, 0, (n-1)!*polcoeff(exp(-x+O(x^n))*sum(k=0, n-1, (k+1)^(k+1)*x^k/k!), n-1))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Robert A. Stump (bee_ess107(AT)yahoo.com), Dec 09 2001
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STATUS
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approved
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