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A260325
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Triangle read by rows: T(n,k) = logarithmic polynomial A_k^(n)(x) evaluated at x=-1.
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4
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1, 2, 1, 5, 2, 2, 16, 9, 6, 6, 65, 28, 12, 24, 24, 326, 185, 140, 60, 120, 120, 1957, 846, 750, 120, 360, 720, 720, 13700, 7777, 2562, 5250, 840, 2520, 5040, 5040, 109601, 47384, 47096, 40656, 1680, 6720, 20160, 40320, 40320, 986410, 559953, 378072, 181944, 365904, 15120, 60480, 181440, 362880, 362880
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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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;
2, 1;
5, 2, 2;
16, 9, 6, 6;
65, 28, 12, 24, 24;
326, 185, 140, 60, 120, 120;
1957, 846, 750, 120, 360, 720, 720;
...
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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+1)!, j=1..(r+1)/n) ;
%*r! ;
end if;
end proc:
for r from 0 to 20 do
for n from 1 to r+1 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+1)!, {j, 1, (n+1)/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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