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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)!. 8
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..36.

FORMULA

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

EXAMPLE

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; ...

PROG

(PARI) T(n, k, q=5)=local(A=Mat(1), B); if(n<k || k<0, 0, for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i || j==1, B[i, j]=1, B[i, j]=(A^q)[i-1, j-1]); )); A=B); B=sum(i=1, #A, -(A^0-A)^i/i); return((n-k)!*B[n+1, k+1]))

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).

Sequence in context: A200615 A318204 A306637 * A113039 A093016 A031018

Adjacent sequences:  A111820 A111821 A111822 * A111824 A111825 A111826

KEYWORD

frac,sign,tabl

AUTHOR

Gottfried Helms and Paul D. Hanna, Aug 22 2005

STATUS

approved

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Last modified September 20 07:21 EDT 2020. Contains 337264 sequences. (Running on oeis4.)