%I #26 Nov 21 2022 08:49:48

%S 1,3,23,223,2800,42576,763220,15734388,366715248,9533817400,

%T 273549419552,8586984241870,292755986184548,10772849583399474,

%U 425587711650564816,17966217346985801150,807152054953801845760,38451365602113352159320,1936082850634342992601636

%N Inverse Euler transform of n^n.

%H Seiichi Manyama, <a href="/A305754/b305754.txt">Table of n, a(n) for n = 1..386</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F Product_{k>=1} 1/(1-x^k)^{a(k)} = Sum_{n>=0} (n * x)^n.

%F a(n) ~ n^n. - _Vaclav Kotesovec_, Oct 09 2019

%e (1-x)^(-1) * (1-x^2)^(-3) * (1-x^3)^(-23) * (1-x^4)^(-223) * ... = 1 + x + 4*x^2 + 27*x^3 + 256*x^4 + ... .

%p # The function EulerInvTransform is defined in A358451.

%p a := EulerInvTransform(n -> n^n):

%p seq(a(n), n = 1..19); # _Peter Luschny_, Nov 21 2022

%t n = 20; s = {};

%t For[i = 1, i <= n, i++, AppendTo[s, i*i^i - Sum[s[[d]]*(i-d)^(i-d), {d, i - 1}]]];

%t Table[Sum[If[Divisible[i, d], MoebiusMu[i/d], 0]*s[[d]], {d, 1, i}]/i, {i, n}] (* _Jean-François Alcover_, May 10 2019 *)

%Y Cf. A000312, A112354, A305787.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 10 2018