A306735 - OEIS

%I #17 Mar 08 2019 03:25:02

%S 1,2,1,3,1,1,4,2,3,1,5,3,2,4,1,6,4,3,5,7,1,7,5,4,3,10,11,1,8,6,5,4,7,

%T 17,18,1,9,7,6,5,4,18,29,29,1,10,8,7,6,5,9,39,51,47,1,11,9,8,7,6,5,28,

%U 73,90,76,1,12,10,9,8,7,6,11,74,127,158,123,1,13,11,10,9,8,7,6,40,164,219,277,199,1

%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. ((k+1-x)*(1-x)^(k-1))/((1-x)^k-x^(k+1)).

%H Seiichi Manyama, <a href="/A306735/b306735.txt">Antidiagonals n = 0..139, flattened</a>

%F A(n,k) = A306646(k*n,k) for k > 0.

%F A(n,k) = (k+1)*A306680(n,k) - A306680(n-1,k) for n > 0.

%e Square array begins:

%e    1,  2,  3,   4,   5,   6,  7,  8, 9, ...

%e    1,  1,  2,   3,   4,   5,  6,  7, 8, ...

%e    1,  3,  2,   3,   4,   5,  6,  7, 8, ...

%e    1,  4,  5,   3,   4,   5,  6,  7, 8, ...

%e    1,  7, 10,   7,   4,   5,  6,  7, 8, ...

%e    1, 11, 17,  18,   9,   5,  6,  7, 8, ...

%e    1, 18, 29,  39,  28,  11,  6,  7, 8, ...

%e    1, 29, 51,  73,  74,  40, 13,  7, 8, ...

%e    1, 47, 90, 127, 164, 125, 54, 15, 8, ...

%Y Columns 0-2 give A000012, A000032, A259967.

%Y Cf. A306646, A306680.

%K nonn,tabl

%O 0,2

%A _Seiichi Manyama_, Mar 06 2019