A096035 - OEIS

%I #16 Mar 11 2015 07:26:59

%S 1,5,2,21,15,3,85,84,30,4,341,425,210,50,5,1365,2046,1275,420,75,6,

%T 5461,9555,7161,2975,735,105,7,21845,43688,38220,19096,5950,1176,140,

%U 8,87381,196605,196596,114660,42966,10710,1764,180,9,349525,873810,983025

%N 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 Alois P. Heinz, <a href="/A096035/b096035.txt">Rows n = 1..141, flattened</a>

%e Triangle begins:

%e 1;

%e 5,       2;

%e 21,     15,    3;

%e 85,     84,   30,   4;

%e 341,   425,  210,  50,  5;

%e 1365, 2046, 1275, 420, 75,  6;

%p 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 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 Cf. A007318. First column gives A002450. Row sums give A016127.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Jun 17 2004

%E Edited and more terms from _Alois P. Heinz_, Oct 07 2009