A306154 - OEIS

%I #11 Jun 23 2018 15:27:12

%S -1,3,-23,226,-2800,42576,-763220,15734614,-366715248,9533817400,

%T -273549419552,8586984284446,-292755986184548,10772849583399474,

%U -425587711650564816,17966217347001535764,-807152054953801845760,38451365602113352159320,-1936082850634342992601636

%N Inverse Weigh transform of (-n)^n.

%H Alois P. Heinz, <a href="/A306154/b306154.txt">Table of n, a(n) for n = 1..386</a>

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

%e (1+x)^(-1)*(1+x^2)^3*(1+x^3)^(-23)*(1+x^4)^226* ... = 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

%Y Cf. A000312, A306152.

%K sign

%O 1,2

%A _Seiichi Manyama_, Jun 23 2018