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A096034 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^3-M)/2, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

%I A096034 #11 May 24 2016 03:10:56
%S A096034 1,4,2,13,12,3,40,52,24,4,121,200,130,40,5,364,726,600,260,60,6,1093,
%T A096034 2548,2541,1400,455,84,7,3280,8744,10192,6776,2800,728,112,8,9841,
%U A096034 29520,39348,30576,15246,5040,1092,144,9,29524,98410,147600,131160,76440
%N A096034 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^3-M)/2, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.
%e A096034 Triangle begins:
%e A096034 1
%e A096034 4 2
%e A096034 13 12 3
%e A096034 40 52 24 4
%e A096034 121 200 130 40 5
%e A096034 364 726 600 260 60 6
%p A096034 P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^3-M)/2 end: T:= (n, k)-> P(n+1)[n+1, k]: seq(seq(T(n, k), k=1..n), n=1..11); # _Alois P. Heinz_, Oct 07 2009
%t A096034 max = 10; M = Table[If[k > n, 0, Binomial[n, k]], {n, 0, max}, {k, 0, max} ];
%t A096034 T = (M.M.M - M)/2;
%t A096034 Table[T[[n + 1]][[1 ;; n]], {n, 1, max}] // Flatten (* _Jean-François Alcover_, May 24 2016 *)
%Y A096034 Cf. A007318. First column gives A003462. Row sums give A006516.
%K A096034 nonn,tabl
%O A096034 1,2
%A A096034 _Gary W. Adamson_, Jun 17 2004
%E A096034 Edited with more terms by _Alois P. Heinz_, Oct 07 2009