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%I #11 Jan 28 2015 04:10:58
%S 1,9,2,73,27,3,585,292,54,4,4681,2925,730,90,5,37449,28086,8775,1460,
%T 135,6,299593,262143,98301,20475,2555,189,7,2396745,2396744,1048572,
%U 262136,40950,4088,252,8,19173961,21570705,10785348,3145716,589806
%N Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^8-M)/7, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.
%e Triangle begins:
%e 1
%e 9 2
%e 73 27 3
%e 585 292 54 4
%e 4681 2925 730 90 5
%e 37449 28086 8775 1460 135 6
%p P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^8-M)/7 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 P[n_] := P[n] = With[{M = Array[Binomial[#1-1, #2-1]&, {n, n}]}, (MatrixPower[M, 8] - M)/7]; 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_ *)
%Y Cf. A007318. First column gives A023001. Row sums give A016133.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Jun 17 2004
%E Edited with more terms by _Alois P. Heinz_, Oct 07 2009
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