A111823 Matrix log of triangle A111820, which shifts columns left and up under matrix 5th power; these terms are the result of multiplying each element in row n and column k by (n-k)!.

0, 1, 0, -3, 5, 0, 16, -15, 25, 0, 2814, 80, -75, 125, 0, -1092180, 14070, 400, -375, 625, 0, -3603928080, -5460900, 70350, 2000, -1875, 3125, 0, 58978973128440, -18019640400, -27304500, 351750, 10000, -9375, 15625, 0, 5974833380453777520

Offset: 0

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Keywords

• frac
• sign
• tabl

Comments

Column k equals 5^k multiplied by column 0 (A111824) when ignoring zeros above the diagonal.

Examples

			Matrix log of A111820, with factorial denominators, begins:
0;
1/1!, 0;
-3/2!, 5/1!, 0;
16/3!, -15/2!, 25/1!, 0;
2814/4!, 80/3!, -75/2!, 125/1!, 0;
-1092180/5!, 14070/4!, 400/3!, -375/2!, 625/1!, 0; ...
		

Crossrefs

Cf. A111820, A111824 (column 0); log matrices: A110504 (q=-1), A111813 (q=2), A111815 (q=3), A111818 (q=4), A111828 (q=6), A111833 (q=7), A111838 (q=8).

Programs

PARI

T(n,k,q=5)=local(A=Mat(1),B);if(n
				

Formula

T(n, k) = 5^k*T(n-k, 0) = A111824(n-k) for n>=k>=0.