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A305754 Inverse Euler transform of n^n.

%I A305754 #26 Nov 21 2022 08:49:48
%S A305754 1,3,23,223,2800,42576,763220,15734388,366715248,9533817400,
%T A305754 273549419552,8586984241870,292755986184548,10772849583399474,
%U A305754 425587711650564816,17966217346985801150,807152054953801845760,38451365602113352159320,1936082850634342992601636
%N A305754 Inverse Euler transform of n^n.
%H A305754 Seiichi Manyama, <a href="/A305754/b305754.txt">Table of n, a(n) for n = 1..386</a>
%H A305754 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A305754 Product_{k>=1} 1/(1-x^k)^{a(k)} = Sum_{n>=0} (n * x)^n.
%F A305754 a(n) ~ n^n. - _Vaclav Kotesovec_, Oct 09 2019
%e A305754 (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 A305754 # The function EulerInvTransform is defined in A358451.
%p A305754 a := EulerInvTransform(n -> n^n):
%p A305754 seq(a(n), n = 1..19); # _Peter Luschny_, Nov 21 2022
%t A305754 n = 20; s = {};
%t A305754 For[i = 1, i <= n, i++, AppendTo[s, i*i^i - Sum[s[[d]]*(i-d)^(i-d), {d, i - 1}]]];
%t A305754 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 A305754 Cf. A000312, A112354, A305787.
%K A305754 nonn
%O A305754 1,2
%A A305754 _Seiichi Manyama_, Jun 10 2018