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A285192 Array read by antidiagonals: T(n,k) = n*k*(3+n*k)/2 (n >= 0, k >= 0).

%I A285192 #15 Jul 09 2025 04:43:28
%S A285192 0,0,0,0,2,0,0,5,5,0,0,9,14,9,0,0,14,27,27,14,0,0,20,44,54,44,20,0,0,
%T A285192 27,65,90,90,65,27,0,0,35,90,135,152,135,90,35,0,0,44,119,189,230,230,
%U A285192 189,119,44,0,0,54,152,252,324,350,324,252,152,54,0
%N A285192 Array read by antidiagonals: T(n,k) = n*k*(3+n*k)/2 (n >= 0, k >= 0).
%H A285192 Robert Israel, <a href="/A285192/b285192.txt">Table of n, a(n) for n = 0..10152</a>
%F A285192 G.f. as array: xy (2-x-y+2xy)/((1-x)^3 (1-y)^3). - _Robert Israel_, Apr 26 2017
%e A285192 Array begins:
%e A285192 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
%e A285192 [0, 2, 5, 9, 14, 20, 27, 35, 44, 54, ...]
%e A285192 [0, 5, 14, 27, 44, 65, 90, 119, 152, 189, ...]
%e A285192 [0, 9, 27, 54, 90, 135, 189, 252, 324, 405, ...]
%e A285192 [0, 14, 44, 90, 152, 230, 324, 434, 560, 702, ...]
%e A285192 [0, 20, 65, 135, 230, 350, 495, 665, 860, 1080, ...]
%e A285192 [0, 27, 90, 189, 324, 495, 702, 945, 1224, 1539, ...]
%e A285192 ...
%p A285192 T:= (n,k) -> n*k*(3+n*k)/2:
%p A285192 seq(seq(T(k,n-k),k=0..n),n=0..10); # _Robert Israel_, Apr 26 2017
%t A285192 Table[# k (3 + # k)/2 &[n - k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* _Michael De Vlieger_, Apr 26 2017 *)
%Y A285192 Row 1 is A000096, row 2 is A014106, etc.
%K A285192 nonn,tabl,easy
%O A285192 0,5
%A A285192 _N. J. A. Sloane_, Apr 26 2017, based on an email message from _Andras W. Ferencz_