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Triangle T(n,m) = A008292(n,m)*binomial(n-1,m-1) read by rows.
4

%I #7 Apr 16 2014 15:30:30

%S 1,1,1,1,8,1,1,33,33,1,1,104,396,104,1,1,285,3020,3020,285,1,1,720,

%T 17865,48320,17865,720,1,1,1729,90153,546665,546665,90153,1729,1,1,

%U 4016,409024,4941104,10933300,4941104,409024,4016,1,1,9117,1722240,38236128

%N Triangle T(n,m) = A008292(n,m)*binomial(n-1,m-1) read by rows.

%C Row sums are A104098(n-1). [Jun 30 2010]

%H Reinhard Zumkeller, <a href="/A141686/b141686.txt">Rows n = 1..125 of table, flattened</a>

%F T(n,m)=T(n,n+1-m).

%e 1;

%e 1, 1;

%e 1, 8, 1;

%e 1, 33, 33, 1;

%e 1, 104, 396, 104, 1;

%e 1, 285, 3020, 3020, 285, 1;

%e 1, 720, 17865, 48320, 17865, 720, 1;

%e 1, 1729, 90153, 546665, 546665, 90153, 1729, 1;

%e 1, 4016, 409024, 4941104, 10933300, 4941104, 409024, 4016, 1;

%e 1, 9117, 1722240, 38236128, 165104604, 165104604, 38236128, 1722240, 9117, 1;

%t (*Recurrence*) A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (n - k + 1)A[n - 1, k - 1] + k A[n - 1, k]; Table[Table[A[n, k]*Binomial[n - 1, k - 1], {k, 1, n}], {n, 1, 10}]; Flatten[%]

%o (Haskell)

%o a141686 n k = a141686_tabl !! (n-1) !! (k-1)

%o a141686_row n = a141686_tabl !! (n-1)

%o a141686_tabl = zipWith (zipWith (*)) a007318_tabl a008292_tabl

%o -- _Reinhard Zumkeller_, Apr 16 2014

%Y Cf. A008292.

%Y Cf. A007318.

%K nonn,tabl

%O 1,5

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 08 2008

%E keyword:tabl inserted, indices corrected by the Assoc. Eds. of the OEIS, Jun 30 2010