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%I #11 Sep 08 2022 08:45:17
%S 1,1,1,1,2,1,1,3,3,1,1,4,7,4,1,1,5,13,15,5,1,1,6,21,40,31,6,1,1,7,31,
%T 85,121,63,7,1,1,8,43,156,341,364,127,8,1,1,9,57,259,781,1365,1093,
%U 255,9,1,1,10,73,400,1555,3906,5461,3280,511,10,1,1,11,91,585,2801,9331,19531,21845,9841,1023,11,1
%N Triangle T(n,k) = Sum_{j=0..k} (n-k)^(k-j), read by rows.
%C Reverse of triangle A104878.
%H G. C. Greubel, <a href="/A104881/b104881.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n, k) = Sum_{j=0..k} (n-k)^(k-j).
%F Sum_{k=0..n} T(n, k) = A104879(n).
%F Sum_{k=0..floor(n/2)} T(k, n-k) = A104882(n).
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 3, 3, 1;
%e 1, 4, 7, 4, 1;
%e 1, 5, 13, 15, 5, 1;
%t T[n_, k_]:= If[k==n, 1, Sum[(n-k)^(k-j), {j,0,k}]];
%t Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jun 15 2021 *)
%o (Magma) [(&+[ (n-k)^(k-j): j in [0..k]]): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jun 15 2021
%o (Sage) flatten([[sum((n-k)^(k-j) for j in (0..k)) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 15 2021
%Y Cf. A104878, A104879 (row sums), A104882 (diagonal sums).
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Mar 28 2005