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A096043 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^9-M)/8, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

%I A096043 #12 Jan 28 2015 04:11:37
%S A096043 1,10,2,91,30,3,820,364,60,4,7381,4100,910,100,5,66430,44286,12300,
%T A096043 1820,150,6,597871,465010,155001,28700,3185,210,7,5380840,4782968,
%U A096043 1860040,413336,57400,5096,280,8,48427561,48427560,21523356,5580120,930006
%N A096043 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^9-M)/8, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.
%e A096043 Triangle begins:
%e A096043 1
%e A096043 10 2
%e A096043 91 30 3
%e A096043 820 364 60 4
%e A096043 7381 4100 910 100 5
%e A096043 66430 44286 12300 1820 150 6
%p A096043 P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^9-M)/8 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 A096043 P[n_] := P[n] = With[{M = Array[Binomial[#1-1, #2-1]&, {n, n}]}, (MatrixPower[M, 9] - M)/8]; 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 A096043 Cf. A007318. First column gives A002452. Row sums give A016134.
%K A096043 nonn,tabl
%O A096043 1,2
%A A096043 _Gary W. Adamson_, Jun 17 2004
%E A096043 Edited with more terms by _Alois P. Heinz_, Oct 07 2009