A136572 - OEIS

%I #15 Mar 27 2022 19:19:47

%S 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 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 0,0,0,0,0,3628800,0,0,0,0,0,0,0,0,0,0,0,39916800

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

%C A136572 * A007318 = A021012(unsigned). A007318 * A136572 = A008279.

%H Reinhard Zumkeller, <a href="/A136572/b136572.txt">Rows n = 0..100 of triangle, flattened</a>

%F Triangle, n zeros followed by n! T(n,k): n! * 0^(n-k), 0 <= k <= n.

%F As an infinite lower triangular matrix, A000142 (1, 1, 2, 6, 24, 120, ...) in the main diagonal and the rest zeros.

%e First few rows of the triangle:

%e   1;

%e   0, 1;

%e   0, 0, 2;

%e   0, 0, 0, 6;

%e   0, 0, 0, 0, 24;

%e   0, 0, 0, 0,  0, 120;

%e   ...

%t Table[PadLeft[{n!},n+1,0],{n,0,20}]//Flatten (* _Harvey P. Dale_, Oct 22 2016 *)

%o (Haskell)

%o a136572 n k = a136572_tabl !! n !! k

%o a136572_row n = a136572_tabl !! n

%o a136572_tabl = map fst $ iterate f ([1], 1) where

%o    f (row, i) = (0 : map (* i) row, i + 1)

%o -- _Reinhard Zumkeller_, Nov 18 2012

%Y Cf. A000142, A021012, A008279.

%K nonn,tabl

%O 0,6

%A _Gary W. Adamson_, Jan 07 2008