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%I #20 Oct 21 2021 21:14:59
%S 1,1,3,1,11,7,1,50,85,15,1,274,1660,575,31,1,1764,48076,46760,3661,63,
%T 1,13068,1942416,6998824,1217776,22631,127,1,109584,104587344,
%U 1744835904,929081776,30480800,137845,255,1,1026576,7245893376,673781602752,1413470290176,117550462624,747497920,833375,511
%N Triangle of differences of reciprocals of unity.
%D F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
%H Alois P. Heinz, <a href="/A008969/b008969.txt">Rows n = 1..45, flattened</a>
%e Triangle T(n,k) begins:
%e 1;
%e 1, 3;
%e 1, 11, 7;
%e 1, 50, 85, 15;
%e 1, 274, 1660, 575, 31;
%e 1, 1764, 48076, 46760, 3661, 63;
%e 1, 13068, 1942416, 6998824, 1217776, 22631, 127;
%e 1, 109584, 104587344, 1744835904, 929081776, 30480800, 137845, 255;
%e ...
%p T:= (n,k)-> `if`(k<=n, (n-k+2)!^k *
%p add((-1)^(j+1)*binomial(n-k+2, j)/ j^k, j=1..n-k+2), 0):
%p seq(seq(T(n,k), k=0..n), n=0..7); # _Alois P. Heinz_, Sep 05 2008
%t 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_ *)
%Y Cf. A001236, A001237, A001238, A001240, A001241, A001242.
%Y Columns include A000254, A000424, A001236, A001237, A001238. Right-hand columns include A000225, A001240, A001241, A001242.
%K nonn,tabl
%O 1,3
%A _N. J. A. Sloane_.
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