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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)!. 6
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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; ...

PROG

(PARI) L(n, k, q=4)=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, B[i, j]=1, if(j==1, B[i, j]=(A^q)[i-1, 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. A111845 (triangle), A111849 (column 0), A111818 (variant).

Sequence in context: A006805 A030045 A126089 * A204384 A102412 A260043

Adjacent sequences:  A111845 A111846 A111847 * A111849 A111850 A111851

KEYWORD

frac,sign,tabl

AUTHOR

Paul D. Hanna, Aug 23 2005

STATUS

approved

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Last modified September 29 18:27 EDT 2020. Contains 337432 sequences. (Running on oeis4.)