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A136572 Triangle read by rows: row n consists of n zeros followed by n!.

%I A136572 #15 Mar 27 2022 19:19:47
%S A136572 1,0,1,0,0,2,0,0,0,6,0,0,0,0,24,0,0,0,0,0,120,0,0,0,0,0,0,720,0,0,0,0,
%T A136572 0,0,0,5040,0,0,0,0,0,0,0,0,40320,0,0,0,0,0,0,0,0,0,362880,0,0,0,0,0,
%U A136572 0,0,0,0,0,3628800,0,0,0,0,0,0,0,0,0,0,0,39916800
%N A136572 Triangle read by rows: row n consists of n zeros followed by n!.
%C A136572 A136572 * A007318 = A021012(unsigned). A007318 * A136572 = A008279.
%H A136572 Reinhard Zumkeller, <a href="/A136572/b136572.txt">Rows n = 0..100 of triangle, flattened</a>
%F A136572 Triangle, n zeros followed by n! T(n,k): n! * 0^(n-k), 0 <= k <= n.
%F A136572 As an infinite lower triangular matrix, A000142 (1, 1, 2, 6, 24, 120, ...) in the main diagonal and the rest zeros.
%e A136572 First few rows of the triangle:
%e A136572   1;
%e A136572   0, 1;
%e A136572   0, 0, 2;
%e A136572   0, 0, 0, 6;
%e A136572   0, 0, 0, 0, 24;
%e A136572   0, 0, 0, 0,  0, 120;
%e A136572   ...
%t A136572 Table[PadLeft[{n!},n+1,0],{n,0,20}]//Flatten (* _Harvey P. Dale_, Oct 22 2016 *)
%o A136572 (Haskell)
%o A136572 a136572 n k = a136572_tabl !! n !! k
%o A136572 a136572_row n = a136572_tabl !! n
%o A136572 a136572_tabl = map fst $ iterate f ([1], 1) where
%o A136572    f (row, i) = (0 : map (* i) row, i + 1)
%o A136572 -- _Reinhard Zumkeller_, Nov 18 2012
%Y A136572 Cf. A000142, A021012, A008279.
%K A136572 nonn,tabl
%O A136572 0,6
%A A136572 _Gary W. Adamson_, Jan 07 2008