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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.)