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A062323 Triangle with a(n,n)=1, a(n,k)=(n-1)*a(n-1,k)+a(n-2,k) for n>k.

%I A062323 #8 Jul 26 2023 13:08:26
%S A062323 1,0,1,1,1,1,2,3,2,1,7,10,7,3,1,30,43,30,13,4,1,157,225,157,68,21,5,1,
%T A062323 972,1393,972,421,130,31,6,1,6961,9976,6961,3015,931,222,43,7,1,56660,
%U A062323 81201,56660,24541,7578,1807,350,57,8,1,516901,740785,516901,223884
%N A062323 Triangle with a(n,n)=1, a(n,k)=(n-1)*a(n-1,k)+a(n-2,k) for n>k.
%H A062323 Reinhard Zumkeller, <a href="/A062323/b062323.txt">Rows n = 0..120 of triangle, flattened</a>
%F A062323 a(n, k)=k*a(n, k+1)+a(n, k+2) for n>k.
%e A062323 Triangle starts:
%e A062323 [0] 1;
%e A062323 [1] 0, 1;
%e A062323 [2] 1, 1, 1;
%e A062323 [3] 2, 3, 2, 1;
%e A062323 [4] 7, 10, 7, 3, 1;
%e A062323 [5] 30, 43, 30, 13, 4, 1;
%e A062323 [6] 157, 225, 157, 68, 21, 5, 1;
%e A062323 [7] 972, 1393, 972, 421, 130, 31, 6, 1;
%e A062323 [8] 6961, 9976, 6961, 3015, 931, 222, 43, 7, 1;
%o A062323 (Haskell)
%o A062323 a062323 n k = a062323_tabl !! n !! k
%o A062323 a062323_row n = a062323_tabl !! n
%o A062323 a062323_tabl = map fst $ iterate f ([1], [0,1]) where
%o A062323    f (us, vs) = (vs, ws) where
%o A062323      ws = (zipWith (+) (us ++ [0]) (map (* v) vs)) ++ [1]
%o A062323           where v = last (init vs) + 1
%o A062323 -- _Reinhard Zumkeller_, Mar 05 2013
%Y A062323 Essentially the same as A058294, but more easy seen as a triangle. Columns include A001040, A001053, A058307, A058308, A058309. Other sequences appearing on the right hand side include A000012, A001477, A002061, A034262.
%K A062323 nonn,tabl
%O A062323 0,7
%A A062323 _Henry Bottomley_, Jul 05 2001