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 A292948 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,k) = (-1)^(k+1) * Sum_{i=0..n-1} (-1)^i * binomial(n-1,i) * binomial(i+1,k) * A(n-1-i,k) for n > 0. 8
 1, 1, -1, 1, 1, 2, 1, 0, -1, -5, 1, 0, 1, -2, 15, 1, 0, 0, -3, 9, -52, 1, 0, 0, 1, 9, -4, 203, 1, 0, 0, 0, -4, -40, -95, -877, 1, 0, 0, 0, 1, 10, 210, 414, 4140, 1, 0, 0, 0, 0, -5, -10, -1176, 49, -21147, 1, 0, 0, 0, 0, 1, 15, -105, 7273, -10088, 115975, 1, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Seiichi Manyama, Antidiagonals n = 0..139, flattened EXAMPLE Square array begins:     1,  1,  1,  1, 1, ...    -1,  1,  0,  0, 0, ...     2, -1,  1,  0, 0, ...    -5, -2, -3,  1, 0, ...    15,  9,  9, -4, 1, ... PROG (Ruby) def ncr(n, r)   return 1 if r == 0   (n - r + 1..n).inject(:*) / (1..r).inject(:*) end def A(k, n)   ary = [1]   (1..n).each{|i| ary << (-1) ** (k % 2 + 1) * (0..i - 1).inject(0){|s, j| s + (-1) ** (j % 2) * ncr(i - 1, j) * ncr(j + 1, k) * ary[i - 1 - j]}}   ary end def A292948(n)   a = []   (0..n).each{|i| a << A(i, n - i)}   ary = []   (0..n).each{|i|     (0..i).each{|j|       ary << a[i - j][j]     }   }   ary end p A292948(20) CROSSREFS Columns k=0-5 give: A292935, A003725, A292909, A292910, A292912, A292950. Rows n=0 gives A000012. Main diagonal gives A000012. Cf. A145460. Sequence in context: A266493 A075374 A293024 * A210872 A292973 A220235 Adjacent sequences:  A292945 A292946 A292947 * A292949 A292950 A292951 KEYWORD sign,tabl,look AUTHOR Seiichi Manyama, Sep 27 2017 STATUS approved

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Last modified January 27 01:45 EST 2021. Contains 340443 sequences. (Running on oeis4.)