A091174 - OEIS

%I #15 Jun 13 2017 21:51:33

%S 1,1,1,2,4,10,30,106,420,1818,8530,43430,240208,1439850,9304070,

%T 64403138,474740644,3708087226,30560873242,264810927102,2404843230640,

%U 22825442299962,225893502009054,2326337105570074,24888766556869700,276246054635709850

%N Leftmost column of triangle A091173, in which the n-th row lists the coefficients of the polynomial that generates the n-th diagonal.

%C The leftmost column of A091173 is determined by the condition that the root of each row polynomial is -1.

%C The first negative term occurs at index n=158.

%H Paul D. Hanna, <a href="/A091174/b091174.txt">Table of n, a(n) for n = 0..200</a>

%o (PARI) /* Set MAX to the number of desired terms to compute */

%o MAX=30; M091173=matrix(MAX+1,MAX+1,r,c,if(r==c || c==1,1));

%o A091173(n, k)=M091173[n+1,k+1]=if(n==k, 1, if(n>k && k>0, sum(j=0, n-k, M091173[n-k+1, j+1]*k^j), if(k==0, -sum(j=1, n, A091173(n, j)*(-1)^j))))

%o for(n=0, MAX, for(k=0, n, A091173(n, k));print1(M091173[n+1,1], ", "))

%Y Cf. A091173, A091175.

%K sign

%O 0,4

%A _Paul D. Hanna_, Dec 25 2003