A306152 - OEIS

%I #16 Mar 19 2022 06:43:27

%S 1,4,23,227,2800,42599,763220,15734615,366715248,9533820200,

%T 273549419552,8586984284469,292755986184548,10772849584162694,

%U 425587711650564816,17966217347001535765,807152054953801845760,38451365602113718874568,1936082850634342992601636

%N Inverse Weigh transform of n^n.

%H Alois P. Heinz, <a href="/A306152/b306152.txt">Table of n, a(n) for n = 1..386</a>

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

%F a(n) ~ n^n. - _Vaclav Kotesovec_, Mar 19 2022

%e (1+x)*(1+x^2)^4*(1+x^3)^23*(1+x^4)^227* ... = 1 + x + 4*x^2 + 27*x^3 + 256*x^4 + ... .

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))

%p     end:

%p a:= n-> n^n-b(n, n-1):

%p seq(a(n), n=1..24);  # _Alois P. Heinz_, Jun 23 2018

%t b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,

%t      Sum[Binomial[a[i], j]*b[n - i*j, i - 1], {j, 0, n/i}]]];

%t a[n_] := n^n - b[n, n - 1];

%t Table[a[n], {n, 1, 24}] (* _Jean-François Alcover_, Mar 19 2022, after _Alois P. Heinz_ *)

%Y Cf. A000312, A306154.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 23 2018