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A213170
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E.g.f.: exp(2*(1-exp(x))).
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11
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1, -2, 2, 2, -6, -14, 26, 178, 90, -2382, -9446, 13746, 287194, 998578, -3687782, -56264782, -208446118, 1017677490, 17194912282, 79540574642, -317691584294, -7577787031374, -47958156443238, 77252406086578, 4400217218583642, 39757699729476274, 54538870133137690
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} A048993(n,k)*(-2)^k.
G.f.: 1/(1+2*x/(1-x/(1+2*x/(1-2*x/(1+2*x/(1-3*x/(1+2*x/(1-4*x/(1+2*x/(1-...(continued fraction).
G.f.: 1/Q(0) where Q(k) = 1 + x*(k+1) + x/(1 - 2*x*(k+1)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 07 2013
Lim sup n->infinity (abs(a(n))/n!)^(1/n) / abs(exp(1/LambertW(-n/2)) / LambertW(-n/2)) = 1. - Vaclav Kotesovec, Aug 04 2014
G.f.: Sum_{j>=0} (-2)^j*x^j / Product_{k=1..j} (1 - k*x). - Ilya Gutkovskiy, Apr 06 2019
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MAPLE
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b:= proc(n, m) option remember; `if`(n=0,
(-2)^m, m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
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MATHEMATICA
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CoefficientList[Series[E^(2*(1-E^x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Aug 04 2014 *)
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PROG
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(PARI) x='x+O('x^50); Vec(serlaplace(exp(2*(1-exp(x))))) \\ G. C. Greubel, Nov 15 2017
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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