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A096042 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^8-M)/7, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

%I A096042 #11 Jan 28 2015 04:10:58
%S A096042 1,9,2,73,27,3,585,292,54,4,4681,2925,730,90,5,37449,28086,8775,1460,
%T A096042 135,6,299593,262143,98301,20475,2555,189,7,2396745,2396744,1048572,
%U A096042 262136,40950,4088,252,8,19173961,21570705,10785348,3145716,589806
%N A096042 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^8-M)/7, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.
%e A096042 Triangle begins:
%e A096042 1
%e A096042 9 2
%e A096042 73 27 3
%e A096042 585 292 54 4
%e A096042 4681 2925 730 90 5
%e A096042 37449 28086 8775 1460 135 6
%p A096042 P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^8-M)/7 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 A096042 P[n_] := P[n] = With[{M = Array[Binomial[#1-1, #2-1]&, {n, n}]}, (MatrixPower[M, 8] - M)/7]; 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 A096042 Cf. A007318. First column gives A023001. Row sums give A016133.
%K A096042 nonn,tabl
%O A096042 1,2
%A A096042 _Gary W. Adamson_, Jun 17 2004
%E A096042 Edited with more terms by _Alois P. Heinz_, Oct 07 2009