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A141680 Triangle read by rows: T(n,m) = (n/m)*binomial(n,m) if m divides n, otherwise 0.

%I A141680 #18 Jun 05 2018 22:33:18
%S A141680 1,4,1,9,0,1,16,12,0,1,25,0,0,0,1,36,45,40,0,0,1,49,0,0,0,0,0,1,64,
%T A141680 112,0,140,0,0,0,1,81,0,252,0,0,0,0,0,1,100,225,0,0,504,0,0,0,0,1
%N A141680 Triangle read by rows: T(n,m) = (n/m)*binomial(n,m) if m divides n, otherwise 0.
%C A141680 Row sums are: 1, 5, 10, 29, 26, 122, 50, 317, 334, 830, ... A105862.
%H A141680 G. C. Greubel, <a href="/A141680/b141680.txt">Rows n=1..100 of triangle, flattened</a>
%F A141680 T(n,m) = A126988(n,m)*binomial(n,m).
%F A141680 T(n,1) = n^2. T(n,n) = 1. T(2n,2) = A015237(n).
%e A141680 1;
%e A141680 4, 1;
%e A141680 9, 0, 1;
%e A141680 16, 12, 0, 1;
%e A141680 25, 0, 0, 0, 1;
%e A141680 36, 45, 40, 0, 0, 1;
%e A141680 49, 0, 0, 0, 0, 0, 1;
%e A141680 64, 112, 0, 140, 0, 0, 0, 1;
%e A141680 81, 0, 252, 0, 0, 0, 0, 0, 1;
%e A141680 100, 225, 0, 0, 504, 0, 0, 0, 0, 1;
%t A141680 t[n_, m_] = If[Mod[n, m] == 0, n/m, 0]*Binomial[n, m]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]
%Y A141680 Cf. A015237, A105862, A126988.
%K A141680 nonn,tabl
%O A141680 1,2
%A A141680 _Roger L. Bagula_ and _Gary W. Adamson_, Sep 07 2008