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A260322
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Triangle read by rows: T(n,k) = logarithmic polynomial G_k^(n)(x) evaluated at x=1.
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4
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1, -1, 2, 2, -6, 6, 0, 24, -24, 24, 9, -80, 60, -120, 120, 35, 450, 240, 360, -720, 720, 230, -2142, -2310, -840, 2520, -5040, 5040, 1624, 17696, 9744, 21840, -6720, 20160, -40320, 40320, 13209, -112464, 91224, -184464, 15120, -60480, 181440, -362880, 362880
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. Gives first 10 rows. [Annotated scanned copy]
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EXAMPLE
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Triangle begins:
1;
-1, 2;
2, -6, 6;
0, 24, -24, 24;
9, -80, 60, -120, 120;
35, 450, 240, 360, -720, 720;
230, -2142, -2310, -840, 2520, -5040, 5040;
...
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MAPLE
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if r = 0 then
1 ;
elif n > r+1 then
0 ;
else
add( (-1)^(r-j*n)/(r-j*n)!/j, j=1..(r)/n) ;
%*r! ;
end if;
end proc:
for r from 1 to 20 do
for n from 1 to r do
end do:
printf("\n") ;
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MATHEMATICA
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T[n_, k_] := Which[n == 0, 1, k > n+1, 0, True,
Sum[(-1)^(n-j*k)/(n-j*k)!/j, {j, 1, n/k}]] n!;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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