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A111810 Matrix log of triangle A098539, which shifts columns left and up under matrix square; these terms are the result of multiplying each element in row n and column k by (n-k)!. 3
0, 1, 0, 2, 2, 0, 10, 4, 4, 0, 88, 20, 8, 8, 0, 1096, 176, 40, 16, 16, 0, 11856, 2192, 352, 80, 32, 32, 0, -402480, 23712, 4384, 704, 160, 64, 64, 0, -1891968, -804960, 47424, 8768, 1408, 320, 128, 128, 0, 36024603264, -3783936, -1609920, 94848, 17536, 2816, 640, 256, 256, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Column k equals 2^k times column 0 (A111811) when ignoring zeros above the diagonal.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n, k) = 2^k*T(n-k, 0) = 2^k*A111811(n-k) for n>=k>=0.

EXAMPLE

Matrix log of A098539, with factorial denominators, begins:

0;

1/1!, 0;

2/2!, 2/1!, 0;

10/3!, 4/2!, 4/1!, 0;

88/4!, 20/3!, 8/2!, 8/1!, 0;

1096/5!, 176/4!, 40/3!, 16/2!, 16/1!, 0;

11856/6!, 2192/5!, 352/4!, 80/3!, 32/2!, 32/1!, 0; ...

PROG

(PARI) T(n, k, q=2)=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. A098539 (triangle), A111811 (column 0), A111813 (variant), A111941 (q=-1), A111843 (q=3), A111848 (q=4).

Sequence in context: A117739 A243203 A268652 * A019265 A285539 A285783

Adjacent sequences:  A111807 A111808 A111809 * A111811 A111812 A111813

KEYWORD

frac,sign,tabl

AUTHOR

Paul D. Hanna, Aug 22 2005

STATUS

approved

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Last modified January 19 20:01 EST 2019. Contains 319309 sequences. (Running on oeis4.)