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%I #39 Sep 08 2022 08:44:36
%S 0,1,128,6561,262144,9765625,362797056,13841287201,549755813888,
%T 22876792454961,1000000000000000,45949729863572161,
%U 2218611106740436992,112455406951957393129,5976303958948914397184,332525673007965087890625
%N a(n) = n^(n+5).
%H Vincenzo Librandi, <a href="/A008791/b008791.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 + 52*T + 328*T^2 + 444*T^3 + 120*T^4)*(1-T)^(-11); 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 diagonals of A048993. - _Tom Copeland_, Oct 03 2011
%F E.g.f.: d^5/dx^5 {x^5/(T(x)^5*(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=-4..n): seq(a(n), n=0..20); # _Zerinvary Lajos_, Jan 26 2008
%t Table[n^(n+5),{n,0,20}] (* _Vladimir Joseph Stephan Orlovsky_, Dec 26 2010 *)
%o (Magma) [n^(n+5): n in [0..20]]; // _Vincenzo Librandi_, Jun 11 2013
%o (PARI) vector(20, n, (n-1)^(n+4)) \\ _G. C. Greubel_, Sep 11 2019
%o (Sage) [n^(n+5) for n in (0..20)] # _G. C. Greubel_, Sep 11 2019
%o (GAP) List([0..20], n-> n^(n+5)); # _G. C. Greubel_, Sep 11 2019
%Y Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008788, A008789, A008790.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
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