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A096040 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^6-M)/5, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

%I A096040 #13 May 24 2016 03:11:47
%S A096040 1,7,2,43,21,3,259,172,42,4,1555,1295,430,70,5,9331,9330,3885,860,105,
%T A096040 6,55987,65317,32655,9065,1505,147,7,335923,447896,261268,87080,18130,
%U A096040 2408,196,8,2015539,3023307,2015532,783804,195930,32634,3612,252,9
%N A096040 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^6-M)/5, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.
%e A096040 Triangle begins:
%e A096040 1;
%e A096040 7,       2;
%e A096040 43,     21,    3;
%e A096040 259,   172,   42,   4;
%e A096040 1555, 1295,  430,  70,   5;
%e A096040 9331, 9330, 3885, 860, 105, 6;
%p A096040 P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^6-M)/5 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 A096040 max = 11; M = Table[If[k > n, 0, Binomial[n, k]], {n, 0, max}, {k, 0, max} ];
%t A096040 T = (MatrixPower[M, 6] - M)/5;
%t A096040 Table[T[[n + 1]][[1 ;; n]] , {n, 1, max}] // Flatten (* _Jean-François Alcover_, May 24 2016 *)
%Y A096040 Cf. A007318. First column gives A003464. Row sums give A016130.
%K A096040 nonn,tabl
%O A096040 1,2
%A A096040 _Gary W. Adamson_, Jun 17 2004
%E A096040 Edited with more terms by _Alois P. Heinz_, Oct 07 2009