OFFSET
0,6
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
T(n,k) = n! * Sum_{j=0..floor(n/k)} (-j)^(n-k*j)/(j! * (n-k*j)!) for k > 0. - Seiichi Manyama, Jul 10 2022
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
-1, 1, 0, 0, 0, ...
2, -1, 2, 0, 0, ...
-5, -2, -6, 6, 0, ...
15, 9, 24, -24, 24, ...
PROG
(Ruby)
def f(n)
return 1 if n < 2
(1..n).inject(:*)
end
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) * f(k) * (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 A292973(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 A292973(20)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Sep 27 2017
STATUS
approved