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%I #2 Mar 30 2012 17:27:11
%S 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,
%T 1,7,61,433,2101,4775,1957,1
%N 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.
%C 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.
%H P. Luschny, <a href="http://www.luschny.de/math/seq/variations.html">Variants of Variations</a>.
%e Array begins:
%e [k=0] 1, 1, 1, 1, 1, 1, 1, 1
%e [k=1] 1, 2, 5, 16, 65, 326, 1957, 13700
%e [k=2] 1, 3, 13, 73, 527, 4775, 52589, 683785
%e [k=3] 1, 4, 25, 202, 2101, 27556, 441625, 8393062
%e [k=4] 1, 5, 41, 433, 5885, 101069, 2126545, 53180009
%e [k=5] 1, 6, 61, 796, 13361, 283706, 7391981, 229229536
%e [k=6] 1, 7, 85, 1321, 26395, 667651, 20743837, 767801905
%e [k=7] 1, 8, 113, 2038, 47237, 1386680, 50038129, 2152463090
%p 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);
%Y Cf. A000522, A128195, A128196, A126062.
%K easy,nonn,tabl
%O 0,5
%A _Peter Luschny_, Mar 02 2007
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