A305754 Inverse Euler transform of n^n.

1, 3, 23, 223, 2800, 42576, 763220, 15734388, 366715248, 9533817400, 273549419552, 8586984241870, 292755986184548, 10772849583399474, 425587711650564816, 17966217346985801150, 807152054953801845760, 38451365602113352159320, 1936082850634342992601636

Offset: 1

Author

Seiichi Manyama, Jun 10 2018

Keywords

• nonn

Examples

			(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 + ... .
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..386
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000312, A112354, A305787.

Programs

Maple

# The function EulerInvTransform is defined in A358451.
a := EulerInvTransform(n -> n^n):
seq(a(n), n = 1..19); # Peter Luschny, Nov 21 2022

Mathematica

n = 20; s = {};
For[i = 1, i <= n, i++, AppendTo[s, i*i^i - Sum[s[[d]]*(i-d)^(i-d), {d, i - 1}]]];
Table[Sum[If[Divisible[i, d], MoebiusMu[i/d], 0]*s[[d]], {d, 1, i}]/i, {i, n}] (* Jean-François Alcover, May 10 2019 *)

Formula

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

a(n) ~ n^n. - Vaclav Kotesovec, Oct 09 2019