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%I #11 Jan 28 2015 04:09:51
%S 1,8,2,57,24,3,400,228,48,4,2801,2000,570,80,5,19608,16806,6000,1140,
%T 120,6,137257,137256,58821,14000,1995,168,7,960800,1098056,549024,
%U 156856,28000,3192,224,8,6725601,8647200,4941252,1647072,352926,50400
%N Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^7-M)/6, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.
%e Triangle begins:
%e 1
%e 8 2
%e 57 24 3
%e 400 228 48 4
%e 2801 2000 570 80 5
%e 19608 16806 6000 1140 120 6
%p P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^7-M)/6 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 P[n_] := P[n] = With[{M = Array[Binomial[#1-1, #2-1]&, {n, n}]}, (MatrixPower[M, 7] - M)/6]; T[n_, k_] := P[n+1][[n+1, k]]; Table[ Table[T[n, k], {k, 1, n}], {n, 1, 11}] // Flatten (* _Jean-François Alcover_, Jan 28 2015, after _Alois P. Heinz_ *)
%Y Cf. A007318. First column gives A023000. Row sums give A016131.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Jun 17 2004
%E Edited with more terms by _Alois P. Heinz_, Oct 07 2009
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