A008785 - OEIS

%I #50 Oct 25 2022 19:32:01

%S 1,5,36,343,4096,59049,1000000,19487171,429981696,10604499373,

%T 289254654976,8649755859375,281474976710656,9904578032905937,

%U 374813367582081024,15181127029874798299,655360000000000000000,30041942495081691894741,1457498964228107529355264

%N a(n) = (n+4)^n.

%H Vincenzo Librandi, <a href="/A008785/b008785.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f.(x) for b(n) = n^(n-4) = a(n-4): T - (7/8)*T^2 + (11/36)*T^3 - (1/24)*T^4, where T = T(x) is Euler's tree function (see A000169). - _Len Smiley_, Nov 17 2001

%F E.g.f.: LambertW(-x)^4/(x^4*(1+LambertW(-x))). - _Vladeta Jovovic_, Nov 07 2003

%F E.g.f.: (1/3)*d/dx(LambertW(-x)/(-x))^3. - _Wolfdieter Lang_, Oct 25 2022

%t Table[(n+4)^n,{n,0,20}] (* _Vladimir Joseph Stephan Orlovsky_, Dec 26 2010 *)

%o (Magma) [(n+4)^n: n in [0..20]]; // _Vincenzo Librandi_, Jun 11 2013

%o (PARI) vector(20, n, (n+3)^(n-1)) \\ _G. C. Greubel_, Nov 09 2017

%o (Sage) [(n+4)^n for n in (0..20)] # _G. C. Greubel_, Sep 11 2019

%o (GAP) List([0..20], n-> (n+4)^n); # _G. C. Greubel_, Sep 11 2019

%Y Cf. A000169, A000272, A000312, A007778, A007830, A008786, A008787, A008788, A008789, A008790, A008791.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_