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

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, 7, 13, 77, 379, 1027, 1217, 385, 7, 8, 15, 104, 653, 2504, 5123, 4376, 897, 8, 9, 17, 135, 1035, 5189, 15629, 24579, 15311, 2049, 9, 10, 19, 170, 1543, 9610, 38885, 93754, 114691, 52490, 4609, 10

Offset: 0

Author

Juri-Stepan Gerasimov, Nov 30 2016

Keywords

• nonn
• tabl
• easy

Examples

			As an infinite triangular array:
0
1   1
2   3   2
3   5   9    3
4   7  20   25     4
5   9  35   83    65      5
As an infinite square array (matrix):
0   1   2    3     4      5
1   3   9   25    65    161
2   5  20   83   326   1217
3   7  35  195  1027   5123
4   9  54  379  2504  15629
5  11  77  653  5189  38885
		

Crossrefs

Cf. A002064.

Cf. Triangles of order m: A003056 (m = -k), A059036 (m = 1-k).

Programs

Magma

/* As triangle */ [[k*(n-k+1)^k+n-k: k in [0..n]]: n in [0..10]];

Maple

A278910 := proc(n,k)
    k*(n-k+1)^k+n-k ;
end proc:
seq(seq(A278910(n,k),k=0..n),n=0..10) ; # R. J. Mathar, Dec 02 2016