A008969 Triangle of differences of reciprocals of unity.

1, 1, 3, 1, 11, 7, 1, 50, 85, 15, 1, 274, 1660, 575, 31, 1, 1764, 48076, 46760, 3661, 63, 1, 13068, 1942416, 6998824, 1217776, 22631, 127, 1, 109584, 104587344, 1744835904, 929081776, 30480800, 137845, 255, 1, 1026576, 7245893376, 673781602752, 1413470290176, 117550462624, 747497920, 833375, 511

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) begins:
  1;
  1,      3;
  1,     11,         7;
  1,     50,        85,         15;
  1,    274,      1660,        575,        31;
  1,   1764,     48076,      46760,      3661,       63;
  1,  13068,   1942416,    6998824,   1217776,    22631,    127;
  1, 109584, 104587344, 1744835904, 929081776, 30480800, 137845, 255;
  ...
		

References

• F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.

Links

• Alois P. Heinz, Rows n = 1..45, flattened

Crossrefs

Cf. A001236, A001237, A001238, A001240, A001241, A001242.

Columns include A000254, A000424, A001236, A001237, A001238. Right-hand columns include A000225, A001240, A001241, A001242.

Programs

Maple

T:= (n,k)-> `if`(k<=n, (n-k+2)!^k *
     add((-1)^(j+1)*binomial(n-k+2, j)/ j^k, j=1..n-k+2), 0):
seq(seq(T(n,k), k=0..n), n=0..7); # Alois P. Heinz, Sep 05 2008

Mathematica

T[n_, k_] := If[k <= n, (n-k+2)!^k*Sum[(-1)^(j+1)*Binomial[n-k+2, j]/j^k, {j, 1, n-k+2}], 0]; Table[Table[T[n, k], {k, 0, n}], {n, 0, 7}] // Flatten (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *)