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.
1, 5, 2, 21, 15, 3, 85, 84, 30, 4, 341, 425, 210, 50, 5, 1365, 2046, 1275, 420, 75, 6, 5461, 9555, 7161, 2975, 735, 105, 7, 21845, 43688, 38220, 19096, 5950, 1176, 140, 8, 87381, 196605, 196596, 114660, 42966, 10710, 1764, 180, 9, 349525, 873810, 983025
Offset: 1
Examples
Triangle begins: 1; 5, 2; 21, 15, 3; 85, 84, 30, 4; 341, 425, 210, 50, 5; 1365, 2046, 1275, 420, 75, 6;
Links
- Alois P. Heinz, Rows n = 1..141, flattened
Programs
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Maple
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
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Mathematica
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 *)
Extensions
Edited and more terms from Alois P. Heinz, Oct 07 2009