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A096035 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^4-M)/3, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

%I A096035 #16 Mar 11 2015 07:26:59
%S A096035 1,5,2,21,15,3,85,84,30,4,341,425,210,50,5,1365,2046,1275,420,75,6,
%T A096035 5461,9555,7161,2975,735,105,7,21845,43688,38220,19096,5950,1176,140,
%U A096035 8,87381,196605,196596,114660,42966,10710,1764,180,9,349525,873810,983025
%N A096035 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^4-M)/3, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.
%H A096035 Alois P. Heinz, <a href="/A096035/b096035.txt">Rows n = 1..141, flattened</a>
%e A096035 Triangle begins:
%e A096035 1;
%e A096035 5,       2;
%e A096035 21,     15,    3;
%e A096035 85,     84,   30,   4;
%e A096035 341,   425,  210,  50,  5;
%e A096035 1365, 2046, 1275, 420, 75,  6;
%p A096035 P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^4-M)/3 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 A096035 rows=11; M[n_] := M[n] = Array[Binomial, {n, n}, {0, 0}]; P[n_] := (MatrixPower[ M[n], 4] - M[n])/3; Table[P[rows+1][[n+1, 1 ;; n]], {n, 1, rows}] // Flatten (* _Jean-François Alcover_, Mar 11 2015 *)
%Y A096035 Cf. A007318. First column gives A002450. Row sums give A016127.
%K A096035 nonn,tabl
%O A096035 1,2
%A A096035 _Gary W. Adamson_, Jun 17 2004
%E A096035 Edited and more terms from _Alois P. Heinz_, Oct 07 2009