A260322
Triangle read by rows: T(n,k) = logarithmic polynomial G_k^(n)(x) evaluated at x=1.
Original entry on oeis.org
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
Offset: 1
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;
...
- J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. Gives first 10 rows. [Annotated scanned copy]
-
A260322 := proc(n,r)
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
printf("%a,",A260322(n,r)) ;
end do:
printf("\n") ;
end do: # R. J. Mathar, Jul 24 2015
-
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!;
Table[T[n, k], {n, 1, 9}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 30 2023 *)
A260323
Triangle read by rows: T(n,k) = logarithmic polynomial G_k^(n)(x) evaluated at x=-1.
Original entry on oeis.org
1, 3, 2, 8, 6, 6, 24, 24, 24, 24, 89, 80, 60, 120, 120, 415, 450, 480, 360, 720, 720, 2372, 2142, 2730, 840, 2520, 5040, 5040, 16072, 17696, 10416, 21840, 6720, 20160, 40320, 40320, 125673, 112464, 151704, 184464, 15120, 60480, 181440, 362880, 362880
Offset: 1
Triangle begins:
1,
3,2,
8,6,6,
24,24,24,24,
89,80,60,120,120,
415,450,480,360,720,720,
2372,2142,2730,840,2520,5040,5040,
...
- J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. Gives first 10 rows. [Annotated scanned copy]
-
A260323 := proc(n,r)
if r = 0 then
1 ;
elif n > r+1 then
0 ;
else
add( 1/(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
printf("%a,",A260323(n,r)) ;
end do:
printf("\n") ;
end do: # R. J. Mathar, Jul 24 2015
-
T[n_, k_] := If[n == 0, 1, If[k > n+1, 0, Sum[1/(n - j*k)!/j, {j, 1, n/k}]]]*n!;
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 25 2023, after R. J. Mathar *)
A260324
Triangle read by rows: T(n,k) = logarithmic polynomial A_k^(n)(x) evaluated at x=1.
Original entry on oeis.org
1, 0, 1, 1, -2, 2, 2, 9, -6, 6, 9, -28, 12, -24, 24, 44, 185, 100, 60, -120, 120, 265, -846, -690, -120, 360, -720, 720, 1854, 7777, 2478, 5250, -840, 2520, -5040, 5040, 14833, -47384, 33656, -40656, 1680, -6720, 20160, -40320, 40320, 133496, 559953, -347832, 181944, 359856, 15120, -60480, 181440, -362880, 362880
Offset: 1
Triangle begins:
1,
0,1,
1,-2,2,
2,9,-6,6,
9,-28,12,-24,24,
44,185,100,60,-120,120,
265,-846,-690,-120,360,-720,720,
...
- J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. Gives first 10 rows. [Annotated scanned copy]
-
A260324 := proc(n,r)
if r = 0 then
1 ;
elif n > r+1 then
0 ;
else
add( (-1)^(r-j*n+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,",A260324(n,r)) ;
end do:
printf("\n") ;
end do: # R. J. Mathar, Jul 24 2015
-
T[n_, k_] := If[k == 0, 1, If[n > k + 1, 0, k! Sum[(-x)^(k - j n + 1)/(k - j n + 1)!, {j, 1, (k + 1)/n}]]];
Table[T[n, k] /. x -> 1, {k, 0, 9}, {n, 1, k + 1}] // Flatten (* Jean-François Alcover, Mar 30 2020 *)
Showing 1-3 of 3 results.