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A111815 Matrix log of triangle A078122, which shifts columns left and up under matrix cube; these terms are the result of multiplying each element in row n and column k by (n-k)!. 8
0, 1, 0, -1, 3, 0, -3, -3, 9, 0, 150, -9, -9, 27, 0, 1236, 450, -27, -27, 81, 0, -2555748, 3708, 1350, -81, -81, 243, 0, -64342116, -7667244, 11124, 4050, -243, -243, 729, 0, 5885700899760, -193026348, -23001732, 33372, 12150, -729, -729, 2187, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Column k equals 3^k multiplied by column 0 (A111816) when ignoring zeros above the diagonal.

LINKS

Table of n, a(n) for n=0..44.

FORMULA

T(n, k) = 3^k*T(n-k, 0) = A111816(n-k) for n>=k>=0.

EXAMPLE

Matrix log of A078122, with factorial denominators, begins:

0;

1/1!, 0;

-1/2!, 3/1!, 0;

-3/3!, -3/2!, 9/1!, 0;

150/4!, -9/3!, -9/2!, 27/1!, 0;

1236/5!, 450/4!, -27/3!, -27/2!, 81/1!, 0;

-2555748/6!, 3708/5!, 1350/4!, -81/3!, -81/2!, 243/1!, 0; ...

PROG

(PARI) T(n, k, q=3)=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. A078122, A111816 (column 0), A111840 (variant); log matrices: A110504 (q=-1), A111813 (q=2), A111818 (q=4), A111823 (q=5), A111828 (q=6), A111833 (q=7), A111838 (q=8).

Sequence in context: A282135 A278923 A210485 * A281269 A210877 A127753

Adjacent sequences:  A111812 A111813 A111814 * A111816 A111817 A111818

KEYWORD

frac,sign,tabl

AUTHOR

Gottfried Helms and Paul D. Hanna, Aug 22 2005

STATUS

approved

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Last modified October 20 07:17 EDT 2018. Contains 316378 sequences. (Running on oeis4.)