A008785 a(n) = (n+4)^n.

1, 5, 36, 343, 4096, 59049, 1000000, 19487171, 429981696, 10604499373, 289254654976, 8649755859375, 281474976710656, 9904578032905937, 374813367582081024, 15181127029874798299, 655360000000000000000, 30041942495081691894741, 1457498964228107529355264

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

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

E.g.f.: LambertW(-x)^4/(x^4*(1+LambertW(-x))). - Vladeta Jovovic, Nov 07 2003

E.g.f.: (1/3)*d/dx(LambertW(-x)/(-x))^3. - Wolfdieter Lang, Oct 25 2022

Mathematica

Table[(n+4)^n, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

Prog

(Magma) [(n+4)^n: n in [0..20]]; // Vincenzo Librandi, Jun 11 2013
(PARI) vector(20, n, (n+3)^(n-1)) \\ G. C. Greubel, Nov 09 2017
(Sage) [(n+4)^n for n in (0..20)] # G. C. Greubel, Sep 11 2019
(GAP) List([0..20], n-> (n+4)^n); # G. C. Greubel, Sep 11 2019

Crossrefs

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

Sequence in context: A261899 A109186 A099391 * A375616 A355494 A081918

Adjacent sequences: A008782 A008783 A008784 * A008786 A008787 A008788

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved