A260325 Triangle read by rows: T(n,k) = logarithmic polynomial A_k^(n)(x) evaluated at x=-1.
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
Offset: 1
Examples
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;
...
Links
- J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. Gives first 10 rows. [Annotated scanned copy]
Crossrefs
Programs
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Maple
A260325 := proc(n,r) 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 printf("%a,",A260325(n,r)) ; end do: printf("\n") ; end do: # R. J. Mathar, Jul 24 2015
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Mathematica
T[n_, k_] := Which[n == 0, 1, k > n+1, 0, True, Sum[1/(n-j*k+1)!, {j, 1, (n+1)/k}]*n!]; Table[T[n, k], {n, 0, 9}, {k, 1, n+1}] // Flatten (* Jean-François Alcover, Apr 25 2023 *)