A136448 - OEIS

%I #8 Mar 06 2013 13:29:21

%S 1,0,1,-4,0,1,0,-13,0,1,64,0,-29,0,1,0,389,0,-54,0,1,-2304,0,1433,0,

%T -90,0,1,0,-21365,0,4079,0,-139,0,1,147456,0,-113077,0,9839,0,-203,0,

%U 1,0,1878021,0,-443476,0,21098,0,-284,0,1,-14745600,0,13185721,0,-1427376,0,41398,0,-384,0,1

%N Triangle T(n,k) with the coefficient [x^k] of the polynomial p(n,x) in row n, column k, where p(n,x) = x*p(n-1,x)-n^2*p(n-2,x).

%C Row sums are s(n) = 1, 1, -3, -12, 36, 336, -960, -17424, 44016, 1455360, -2946240,...

%F p(0,x)=1; p(1,x)=x; p(n,x) = x*p(n-1,x)-n^2*p(n-2,x). T(n,k) = [x^k] p(n,x), 0<=k<=n.

%F Row sums satisfy s(n)-s(n-1)+n^2*s(n-2)=0. - _R. J. Mathar_, Mar 06 2013

%e 1;

%e 0,1;

%e -4,0,1;

%e 0,-13,0,1;

%e 64,0,-29,0,1;

%e 0,389,0,-54,0,1;

%e -2304,0,1433,0,-90,0,1;

%e 0,-21365,0,4079,0,-139,0,1;

%e 147456,0,-113077,0,9839,0,-203,0,1;

%e 0,1878021,0,-443476,0,21098,0,-284,0,1;

%e -14745600,0,13185721,0,-1427376,0,41398,0,-384,0,1;

%Y Cf. A168559 (first subdiagonal)

%K easy,tabl,sign

%O 0,4

%A _Roger L. Bagula_, Mar 19 2008