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%I #43 Sep 08 2022 08:44:36
%S 0,1,32,729,16384,390625,10077696,282475249,8589934592,282429536481,
%T 10000000000000,379749833583241,15407021574586368,665416609183179841,
%U 30491346729331195904,1477891880035400390625,75557863725914323419136
%N a(n) = n^(n+3).
%H Vincenzo Librandi, <a href="/A008789/b008789.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 +8*T +6*T^2)*(1-T)^(-7); where T=T(x) is Euler's tree function (see A000169). - _Len Smiley_, Nov 19 2001
%F See A008517 and A134991 for similar e.g.f.s and diagonals of A048993. - _Tom Copeland_, Oct 03 2011
%F E.g.f.: d^3/dx^3 {x^3/(T(x)^3*(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
%F a(n) = n*A008788(n). - _R. J. Mathar_, Oct 31 2015
%p printlevel := -1; a := [0]; T := x->-LambertW(-x); f := series((T(x)*(1+8*T(x)+6*(T(x))^2)/(1-T(x))^7),x,24); for m from 1 to 23 do a := [op(a),op(2*m-1,f)*m! ] od; print(a); # _Len Smiley_, Nov 19 2001
%t Table[n^(n+3),{n,0,20}](* _Vladimir Joseph Stephan Orlovsky_, Dec 26 2010 *)
%o (Magma) [n^(n+3): n in [0..20]]; // _Vincenzo Librandi_, Jun 11 2013
%o (PARI) vector(20, n, (n-1)^(n+2)) \\ _G. C. Greubel_, Sep 11 2019
%o (Sage) [n^(n+3) for n in (0..20)] # _G. C. Greubel_, Sep 11 2019
%o (GAP) List([0..20], n-> n^(n+3)); # _G. C. Greubel_, Sep 11 2019
%Y Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008788, A008790, A008791.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
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