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A111813 Matrix log of triangle A078121, 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)!. 8
0, 1, 0, 0, 2, 0, -2, 0, 4, 0, 0, -4, 0, 8, 0, 216, 0, -8, 0, 16, 0, 0, 432, 0, -16, 0, 32, 0, -568464, 0, 864, 0, -32, 0, 64, 0, 0, -1136928, 0, 1728, 0, -64, 0, 128, 0, 36058658688, 0, -2273856, 0, 3456, 0, -128, 0, 256, 0, 0, 72117317376, 0, -4547712, 0, 6912, 0, -256, 0, 512, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Column k equals 2^k multiplied by column 0 (A111814) when ignoring zeros above the diagonal.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n, k) = 2^k*T(n-k, 0) = A111814(n-k) for n>=k>=0.

EXAMPLE

Matrix log of A078121, with factorial denominators, begins:

0;

1/1!, 0;

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

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

0/4!, -4/3!, 0/2!, 8/1!, 0;

216/5!, 0/4!, -8/3!, 0/2!, 16/1!, 0;

0/6!, 432/5!, 0/4!, -16/3!, 0/2!, 32/1!, 0;

-568464/7!, 0/6!, 864/5!, 0/4!, -32/3!, 0/2!, 64/1!, 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 || 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. A078121, A111814 (column 0), A111810 (variant); log matrices: A110504 (q=-1), A111815 (q=3), A111818 (q=4), A111823 (q=5), A111828 (q=6), A111833 (q=7), A111838 (q=8).

Sequence in context: A096500 A231563 A282849 * A167156 A132952 A319998

Adjacent sequences:  A111810 A111811 A111812 * A111814 A111815 A111816

KEYWORD

frac,sign,tabl

AUTHOR

Gottfried Helms and Paul D. Hanna, Aug 22 2005

STATUS

approved

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Last modified July 8 04:16 EDT 2020. Contains 335504 sequences. (Running on oeis4.)