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A104634 Triangle T(n,k) = (k-1-n)*(k-2-n)*(k+2*n)/6, 1<=k<=n.

%I A104634 #11 Sep 08 2022 08:45:17
%S A104634 1,5,2,14,8,3,30,20,11,4,55,40,26,14,5,91,70,50,32,17,6,140,112,85,60,
%T A104634 38,20,7,204,168,133,100,70,44,23,8,285,240,196,154,115,80,50,26,9,
%U A104634 385,330,276,224,175,130,90,56,29,10,506,440,375,312,252,196,145,100,62,32,11,650,572,495,420,348,280,217,160,110,68,35,12,819,728,638,550,465,384
%N A104634 Triangle T(n,k) = (k-1-n)*(k-2-n)*(k+2*n)/6, 1<=k<=n.
%H A104634 G. C. Greubel, <a href="/A104634/b104634.txt">Rows n=1..100 of triangle, flattened</a>
%F A104634 The triangle is created by the matrix product A002260 * A004736, both infinite lower triangular matrices.
%e A104634 The first few rows are:
%e A104634 1;
%e A104634 5, 2;
%e A104634 14, 8, 3;
%e A104634 30, 20, 11, 4;
%e A104634 55, 40, 26, 14, 5;
%e A104634 91, 70, 50, 32, 17, 6;
%e A104634 ...
%p A104634 A104634 := proc(n,k) (k-1-n)*(k-2-n)*(k+2*n)/6 ; end proc:
%p A104634 seq(seq(A104634(n,k),k=1..n),n=1..15) ; # _R. J. Mathar_, Aug 31 2011
%t A104634 Table[(k-1-n)*(k-2-n)*(k+2*n)/6, {n, 1, 20}, {k, 1, n}] // Flatten (* _G. C. Greubel_, Aug 12 2018 *)
%o A104634 (PARI) for(n=1,20, for(k=1,n, print1((k-1-n)*(k-2-n)*(k+2*n)/6, ", "))) \\ _G. C. Greubel_, Aug 12 2018
%o A104634 (Magma) [[(k-1-n)*(k-2-n)*(k+2*n)/6: k in [1..n]]: n in [1..20]]; // _G. C. Greubel_, Aug 12 2018
%Y A104634 Cf. A000330 (column 1), A007290 (column 2), A051925 (column 3), A001296 (row sums), A104633, A000332.
%K A104634 nonn,tabl,easy
%O A104634 1,2
%A A104634 _Gary W. Adamson_, Mar 18 2005
%E A104634 Definition in closed form provided by _R. J. Mathar_, Aug 31 2011