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

1,2

Links

Table of n, a(n) for n=1..55.

J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. Gives first 10 rows. [Annotated scanned copy]

Example

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;
  ...

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

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 *)

Crossrefs

Rows, column sums give A000522, A002747, A002750, A002751.

Main diagonal gives A000142.

Cf. A260322, A260323, A260324.

Sequence in context: A110874 A010253 A065274 * A136262 A162180 A090003

Adjacent sequences: A260322 A260323 A260324 * A260326 A260327 A260328

Keyword

sign,tabl

Author

N. J. A. Sloane, Jul 23 2015

Status

approved