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%I #13 Sep 08 2022 08:46:18
%S 0,1,1,2,3,2,3,5,9,3,4,7,20,25,4,5,9,35,83,65,5,6,11,54,195,326,161,6,
%T 7,13,77,379,1027,1217,385,7,8,15,104,653,2504,5123,4376,897,8,9,17,
%U 135,1035,5189,15629,24579,15311,2049,9,10,19,170,1543,9610,38885,93754,114691,52490,4609,10
%N Triangle of order m: C(n,k) = k*(n-k+1)^(k+m)+n-k, 0 <= k <= n, m = 0, read by rows.
%e As an infinite triangular array:
%e 0
%e 1 1
%e 2 3 2
%e 3 5 9 3
%e 4 7 20 25 4
%e 5 9 35 83 65 5
%e As an infinite square array (matrix):
%e 0 1 2 3 4 5
%e 1 3 9 25 65 161
%e 2 5 20 83 326 1217
%e 3 7 35 195 1027 5123
%e 4 9 54 379 2504 15629
%e 5 11 77 653 5189 38885
%p A278910 := proc(n,k)
%p k*(n-k+1)^k+n-k ;
%p end proc:
%p seq(seq(A278910(n,k),k=0..n),n=0..10) ; # _R. J. Mathar_, Dec 02 2016
%o (Magma) /* As triangle */ [[k*(n-k+1)^k+n-k: k in [0..n]]: n in [0..10]];
%Y Cf. A002064.
%Y Cf. Triangles of order m: A003056 (m = -k), A059036 (m = 1-k).
%K nonn,tabl,easy
%O 0,4
%A _Juri-Stepan Gerasimov_, Nov 30 2016
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