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A305401 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where A(n,k) is Sum_{j=0..floor(n/2)} ((n-j)!/j!)*binomial(n-j,j)*k^(n-2*j). 3

%I

%S 1,1,0,1,1,1,1,2,3,0,1,3,9,10,1,1,4,19,56,43,0,1,5,33,174,457,225,1,1,

%T 6,51,400,2107,4626,1393,0,1,7,73,770,6433,31779,55969,9976,1,1,8,99,

%U 1320,15451,129060,574129,788192,81201,0,1,9,129,2086,31753,387045,3103873,12088488,12667041,740785,1

%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where A(n,k) is Sum_{j=0..floor(n/2)} ((n-j)!/j!)*binomial(n-j,j)*k^(n-2*j).

%H Seiichi Manyama, <a href="/A305401/b305401.txt">Antidiagonals n = 0..139, flattened</a>

%F A(n,k) = k*n*A(n-1,k) + A(n-2,k) for n>1.

%e Square array begins:

%e 1, 1, 1, 1, 1, 1, ...

%e 0, 1, 2, 3, 4, 5, ...

%e 1, 3, 9, 19, 33, 51, ...

%e 0, 10, 56, 174, 400, 770, ...

%e 1, 43, 457, 2107, 6433, 15451, ...

%Y Columns k=0-3 give A059841, A001040(n+1), A036243, A305459.

%Y Rows n=0-2 give A000012, A001477, A058331.

%Y Main diagonal gives A305465.

%Y Cf. A305466.

%K nonn,tabl

%O 0,8

%A _Seiichi Manyama_, Jun 02 2018

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)