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A363436 Array read by ascending antidiagonals: A(n, k) = k*n^2, with k >= 0.

%I A363436 #28 Aug 02 2023 14:40:59
%S A363436 0,0,0,0,1,0,0,4,2,0,0,9,8,3,0,0,16,18,12,4,0,0,25,32,27,16,5,0,0,36,
%T A363436 50,48,36,20,6,0,0,49,72,75,64,45,24,7,0,0,64,98,108,100,80,54,28,8,0,
%U A363436 0,81,128,147,144,125,96,63,32,9,0,0,100,162,192,196,180,150,112,72,36,10,0
%N A363436 Array read by ascending antidiagonals: A(n, k) = k*n^2, with k >= 0.
%F A363436 O.g.f.: x*y*(1 + x)/((1 - x)^3*(1 - y)^2).
%F A363436 E.g.f.: x*y*(1 + x)*exp(x + y).
%F A363436 A(n, k) = n*A004247(n, k).
%e A363436 The array begins:
%e A363436   0,  0,  0,   0,   0,   0,   0, ...
%e A363436   0,  1,  2,   3,   4,   5,   6, ...
%e A363436   0,  4,  8,  12,  16,  20,  24, ...
%e A363436   0,  9, 18,  27,  36,  45,  54, ...
%e A363436   0, 16, 32,  48,  64,  80,  96, ...
%e A363436   0, 25, 50,  75, 100, 125, 150, ...
%e A363436   0, 36, 72, 108, 144, 180, 216, ...
%e A363436   ...
%t A363436 A[n_,k_]:=k n^2; Table[A[n-k,k],{n,0,11},{k,0,n}]//Flatten
%Y A363436 Cf. A000290 (k = 1), A001105 (k = 2), A033428 (k = 3), A016742 (k = 4), A033429 (k = 5), A033581 (k = 6), A033582 (k = 7), A139098 (k = 8), A016766 (k = 9), A033583 (k = 10), A033584 (k = 11), A135453 (k = 12),  A152742 (k = 13), A144555 (k = 14), A064761 (k = 15), A016802 (k = 16), A244630 (k = 17), A195321 (k = 18), A244631 (k = 19), A195322 (k = 20), A064762 (k = 21), A195323 (k = 22), A244632 (k = 23), A195824 (k = 24), A016850 (k = 25), A244633 (k = 26), A244634 (k = 27), A064763 (k = 28), A244635 (k = 29), A244636 (k = 30).
%Y A363436 Cf. A001477 (n = 1), A008586 (n = 2), A008591 (n = 3), A008598 (n = 4), A008607 (n = 5), A044102 (n = 6), A152691 (n = 8).
%Y A363436 Cf. A000007 (n = 0 or k = 0), A000578 (main diagonal), A002415 (antidiagonal sums), A004247.
%K A363436 nonn,easy,tabl
%O A363436 0,8
%A A363436 _Stefano Spezia_, Jul 08 2023