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A104881 Triangle T(n,k) = Sum_{j=0..k} (n-k)^(k-j), read by rows.

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