A096041 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^7-M)/6, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

1, 8, 2, 57, 24, 3, 400, 228, 48, 4, 2801, 2000, 570, 80, 5, 19608, 16806, 6000, 1140, 120, 6, 137257, 137256, 58821, 14000, 1995, 168, 7, 960800, 1098056, 549024, 156856, 28000, 3192, 224, 8, 6725601, 8647200, 4941252, 1647072, 352926, 50400

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Example

Triangle begins:
1
8 2
57 24 3
400 228 48 4
2801 2000 570 80 5
19608 16806 6000 1140 120 6

Maple

P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^7-M)/6 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

Mathematica

P[n_] := P[n] = With[{M = Array[Binomial[#1-1, #2-1]&, {n, n}]}, (MatrixPower[M, 7] - M)/6]; 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 *)

Crossrefs

Cf. A007318. First column gives A023000. Row sums give A016131.

Sequence in context: A273671 A303635 A179315 * A202625 A038280 A260039

Adjacent sequences: A096038 A096039 A096040 * A096042 A096043 A096044

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 17 2004

Extensions

Edited with more terms by Alois P. Heinz, Oct 07 2009

Status

approved