A136448 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).

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, -90, 0, 1, 0, -21365, 0, 4079, 0, -139, 0, 1, 147456, 0, -113077, 0, 9839, 0, -203, 0, 1, 0, 1878021, 0, -443476, 0, 21098, 0, -284, 0, 1, -14745600, 0, 13185721, 0, -1427376, 0, 41398, 0, -384, 0, 1

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..65.

Formula

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.

Row sums satisfy s(n)-s(n-1)+n^2*s(n-2)=0. - R. J. Mathar, Mar 06 2013

Example

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,-90,0,1;
0,-21365,0,4079,0,-139,0,1;
147456,0,-113077,0,9839,0,-203,0,1;
0,1878021,0,-443476,0,21098,0,-284,0,1;
-14745600,0,13185721,0,-1427376,0,41398,0,-384,0,1;

Crossrefs

Cf. A168559 (first subdiagonal)

Sequence in context: A282252 A268367 A117436 * A166318 A166317 A068346

Adjacent sequences: A136445 A136446 A136447 * A136449 A136450 A136451

Keyword

easy,tabl,sign

Author

Roger L. Bagula, Mar 19 2008

Status

approved