A111848 Matrix log of triangle A111845, which shifts columns left and up under matrix 4th power; these terms are the result of multiplying each element in row n and column k by (n-k)!.

0, 1, 0, 4, 4, 0, 56, 16, 16, 0, 1728, 224, 64, 64, 0, -45696, 6912, 896, 256, 256, 0, -159401472, -182784, 27648, 3584, 1024, 1024, 0, 387212983296, -637605888, -731136, 110592, 14336, 4096, 4096, 0, 14722642769657856, 1548851933184, -2550423552, -2924544, 442368, 57344, 16384, 16384, 0

Offset: 0

Author

Paul D. Hanna, Aug 23 2005

Keywords

• frac
• sign
• tabl

Comments

Column k equals 4^k multiplied by column 0 (A111849) when ignoring zeros above the diagonal.

Examples

			Matrix log of A111845, with factorial denominators, begins:
0;
1/1!, 0;
4/2!, 4/1!, 0;
56/3!, 16/2!, 16/1!, 0;
1728/4!, 224/3!, 64/2!, 64/1!, 0;
-45696/5!, 6912/4!, 896/3!, 256/2!, 256/1!, 0; ...
		

Crossrefs

Cf. A111845 (triangle), A111849 (column 0), A111818 (variant).

Programs

PARI

L(n,k,q=4)=local(A=Mat(1),B);if(n
				

Formula

T(n, k) = 4^k*T(n-k, 0) = 4^k*A111844(n-k) for n>=k>=0.