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A293015 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,k) = - Sum_{i=0..n-1} binomial(n-1,i) * binomial(i+1,k) * A(n-1-i,k) for n > 0. 6

%I #11 Sep 30 2017 04:39:51

%S 1,1,-1,1,-1,0,1,0,-1,1,1,0,-1,2,1,1,0,0,-3,9,-2,1,0,0,-1,-3,4,-9,1,0,

%T 0,0,-4,20,-95,-9,1,0,0,0,-1,-10,150,-414,50,1,0,0,0,0,-5,-10,504,49,

%U 267,1,0,0,0,0,-1,-15,105,-343,10088,413,1,0,0,0,0,0,-6

%N Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,k) = - Sum_{i=0..n-1} binomial(n-1,i) * binomial(i+1,k) * A(n-1-i,k) for n > 0.

%H Seiichi Manyama, <a href="/A293015/b293015.txt">Antidiagonals n = 0..139, flattened</a>

%e Square array begins:

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

%e -1, -1, 0, 0, 0, ...

%e 0, -1, -1, 0, 0, ...

%e 1, 2, -3, -1, 0, ...

%e 1, 9, -3, -4, -1, ...

%Y Columns k=0-4 give: A000587, A292952, A292953, A292954, A292955.

%Y Rows n=0 gives A000012.

%Y Cf. A145460.

%K sign,tabl

%O 0,14

%A _Seiichi Manyama_, Sep 28 2017

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Last modified August 13 16:19 EDT 2024. Contains 375142 sequences. (Running on oeis4.)