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%I #53 Sep 08 2022 08:44:36
%S 0,1,16,243,4096,78125,1679616,40353607,1073741824,31381059609,
%T 1000000000000,34522712143931,1283918464548864,51185893014090757,
%U 2177953337809371136,98526125335693359375,4722366482869645213696
%N a(n) = n^(n+2).
%H Vincenzo Librandi, <a href="/A008788/b008788.txt">Table of n, a(n) for n = 0..200</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%F E.g.f.(x): T*(1 + 2*T)*(1-T)^(-5); where T=T(x) is Euler's tree function (see A000169). - _Len Smiley_, Nov 17 2001
%F See A008517 and A134991 for similar e.g.f.s. and A048993. - _Tom Copeland_, Oct 03 2011
%F E.g.f.: d^2/dx^2 {x^2/(T(x)^2*(1-T(x))}, where T(x) = sum {n >= 1} n^(n-1)*x^n/n! is the tree function of A000169. - _Peter Bala_, Aug 05 2012
%e G.f. = x + 16*x^2 + 243*x^3 + 4096*x^4 + 78125*x^5 + 1679616*x^6 + ...
%t Table[n^(n+2), {n,0,20}] (* _Vladimir Joseph Stephan Orlovsky_, Dec 26 2010 *)
%t CoefficientList[Series[LambertW[-x] * (2*LambertW[-x]-1) / (1 + LambertW[-x])^5, {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Dec 20 2014 *)
%o (Magma) [n^(n+2): n in [0..20]]; // _Vincenzo Librandi_, Jun 11 2013
%o (PARI) vector(20, n, (n-1)^(n+1)) \\ _G. C. Greubel_, Nov 14 2017
%o (Sage) [n^(n+2) for n in (0..20)] # _G. C. Greubel_, Sep 11 2019
%o (GAP) List([0..20], n-> n^(n+2)); # _G. C. Greubel_, Sep 11 2019
%Y Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008789, A008790, A008791.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
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