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

0,4

Links

Table of n, a(n) for n=0..65.

Example

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

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

Prog

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

Crossrefs

Cf. A002064.

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

Sequence in context: A251104 A199334 A330903 * A337982 A235669 A118088

Adjacent sequences: A278907 A278908 A278909 * A278911 A278912 A278913

Keyword

nonn,tabl,easy

Author

Juri-Stepan Gerasimov, Nov 30 2016

Status

approved