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%I #15 Nov 03 2023 15:21:48
%S 1,0,1,0,1,6,0,1,11,54,0,1,20,151,680,0,1,37,413,2569,11000,0,1,70,
%T 1128,9450,52431,217392,0,1,135,3104,34416,243255,1251921,5076400,0,1,
%U 264,8637,125248,1113027,7025016,34282879,136761984,0,1,521,24327,457807,5064143,38811015,225930121,1059812993,4175432064,0,1,1034,69334,1685266,23031680,212609518,1465077802,8026643702,36519075583,142469423360
%N T(n,k) = Sum_{j=0..k} (k-j)^n * binomial(n,j).
%H Alois P. Heinz, <a href="/A215080/b215080.txt">Rows n = 0..140, flattened</a>
%F T(n,k) = sum( (k-j)^n * binomial(n,j), j=0..k).
%e Triangle T(n,k) begins:
%e 1;
%e 0, 1;
%e 0, 1, 6;
%e 0, 1, 11, 54;
%e 0, 1, 20, 151, 680;
%e 0, 1, 37, 413, 2569, 11000;
%e 0, 1, 70, 1128, 9450, 52431, 217392;
%e 0, 1, 135, 3104, 34416, 243255, 1251921, 5076400;
%e 0, 1, 264, 8637, 125248, 1113027, 7025016, 34282879, 136761984;
%e ...
%t Flatten[Table[Table[Sum[(k - j)^n*Binomial[n, j], {j, 0, k}], {k, 0, n}], {n, 0, 10}], 1]
%Y Row sums give 215077 (binomial convolution of descending powers).
%Y Main diagonal gives A072034.
%K nonn,tabl
%O 0,6
%A _Olivier Gérard_, Aug 02 2012
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