A128198 Array read by antidiagonals. A scheme of arrangements: ArrScheme(k,n) = VarScheme(k,n-1) + k^n; ArrScheme(k,0) = 1. VarScheme(k,n) = (n*k+1)*(VarScheme(k,n-1) + k^n); VarScheme(k,0) = 1.

1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 13, 16, 1, 1, 5, 25, 73, 65, 1, 1, 6, 41, 202, 527, 326, 1, 1, 7, 61, 433, 2101, 4775, 1957, 1

Offset: 0

Author

Peter Luschny, Mar 02 2007

Keywords

• easy
• nonn
• tabl

Comments

The second row (k=1) is sequence A000522 counting the arrangements of a set with n elements and the third row (k=2) is the sequence A128196. Cf. the scheme of variations A128195.

Examples

			Array begins:
[k=0] 1, 1, 1, 1, 1, 1, 1, 1
[k=1] 1, 2, 5, 16, 65, 326, 1957, 13700
[k=2] 1, 3, 13, 73, 527, 4775, 52589, 683785
[k=3] 1, 4, 25, 202, 2101, 27556, 441625, 8393062
[k=4] 1, 5, 41, 433, 5885, 101069, 2126545, 53180009
[k=5] 1, 6, 61, 796, 13361, 283706, 7391981, 229229536
[k=6] 1, 7, 85, 1321, 26395, 667651, 20743837, 767801905
[k=7] 1, 8, 113, 2038, 47237, 1386680, 50038129, 2152463090
		

Links

• P. Luschny, Variants of Variations.

Crossrefs

Cf. A000522, A128195, A128196, A126062.

Programs

Maple

VarScheme := (k,n) -> `if`(n=0,1,(n*k+1)*(VarScheme(k,n-1)+k^n)); ArrScheme := (k,n) -> `if`(n=0,1, VarScheme(k,n-1)+k^n);