A096043 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^9-M)/8, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

1, 10, 2, 91, 30, 3, 820, 364, 60, 4, 7381, 4100, 910, 100, 5, 66430, 44286, 12300, 1820, 150, 6, 597871, 465010, 155001, 28700, 3185, 210, 7, 5380840, 4782968, 1860040, 413336, 57400, 5096, 280, 8, 48427561, 48427560, 21523356, 5580120, 930006

Offset

1,2

Links

Table of n, a(n) for n=1..41.

Example

Triangle begins:
1
10 2
91 30 3
820 364 60 4
7381 4100 910 100 5
66430 44286 12300 1820 150 6

Maple

P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^9-M)/8 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, 9] - M)/8]; 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 A002452. Row sums give A016134.

Sequence in context: A094715 A213555 A305995 * A001202 A054841 A185076

Adjacent sequences: A096040 A096041 A096042 * A096044 A096045 A096046

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 17 2004

Extensions

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

Status

approved