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A278910 Triangle of order m: C(n,k) = k*(n-k+1)^(k+m)+n-k, 0 <= k <= n, m = 0, read by rows.

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