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%I #34 Sep 08 2022 08:44:36
%S 0,1,64,2187,65536,1953125,60466176,1977326743,68719476736,
%T 2541865828329,100000000000000,4177248169415651,184884258895036416,
%U 8650415919381337933,426878854210636742656,22168378200531005859375
%N a(n) = n^(n+4).
%H Vincenzo Librandi, <a href="/A008790/b008790.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.: T*(1 +22*T +58*T^2 +24*T^3)*(1-T)^(-9); where T is Euler's tree function (see A000169). - _Len Smiley_, Nov 17 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^4/dx^4 {x^4/(T(x)^4*(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
%p a:=n->mul(n,k=-3..n):seq(a(n),n=0..20); # _Zerinvary Lajos_, Jan 26 2008
%t Table[n^(n+4),{n,0,20}](* _Vladimir Joseph Stephan Orlovsky_, Dec 26 2010 *)
%o (Magma) [n^(n+4): n in [0..20]]; // _Vincenzo Librandi_, Jun 11 2013
%o (PARI) vector(20, n, (n-1)^(n+3)) \\ _G. C. Greubel_, Sep 11 2019
%o (Sage) [n^(n+4) for n in (0..20)] # _G. C. Greubel_, Sep 11 2019
%o (GAP) List([0..20], n-> n^(n+4)); # _G. C. Greubel_, Sep 11 2019
%Y Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008788, A008789, A008791.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
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