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A323663 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is Sum_{j=1..n} binomial(j*k, k).

%I A323663 #18 Jan 23 2019 10:10:12
%S A323663 1,1,3,1,7,6,1,21,22,10,1,71,105,50,15,1,253,566,325,95,21,1,925,3256,
%T A323663 2386,780,161,28,1,3433,19489,18760,7231,1596,252,36,1,12871,119713,
%U A323663 154085,71890,17857,2926,372,45,1,48621,748342,1303753,747860,214396,38332,4950,525,55
%N A323663 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is Sum_{j=1..n} binomial(j*k, k).
%H A323663 Seiichi Manyama, <a href="/A323663/b323663.txt">Antidiagonals n = 1..140, flattened</a>
%e A323663 Square array begins:
%e A323663     1,   1,    1,     1,       1,        1, ...
%e A323663     3,   7,   21,    71,     253,      925, ...
%e A323663     6,  22,  105,   566,    3256,    19489, ...
%e A323663    10,  50,  325,  2386,   18760,   154085, ...
%e A323663    15,  95,  780,  7231,   71890,   747860, ...
%e A323663    21, 161, 1596, 17857,  214396,  2695652, ...
%e A323663    28, 252, 2926, 38332,  539028,  7941438, ...
%e A323663    36, 372, 4950, 74292, 1197036, 20212950, ...
%Y A323663 Columns 1-3 give A000217, A002412, A116689.
%Y A323663 Rows 1-3 give A000012, A244174, A029848.
%Y A323663 Main diagonal is A096131.
%Y A323663 Cf. A060539.
%K A323663 nonn,tabl
%O A323663 1,3
%A A323663 _Seiichi Manyama_, Jan 23 2019