160520

Ruby

Π(1 - q^n)(1)

オンライン整数列大辞典の
A010815（http://oeis.org/A010815/list）
と比較し、答え合わせしてみる。

# m次以下を取り出す
def mul(f_ary, b_ary, m)
  s1, s2 = f_ary.size, b_ary.size
  ary = Array.new(s1 + s2 - 1, 0)
  (0..s1 - 1).each{|i|
    (0..s2 - 1).each{|j|
      ary[i + j] += f_ary[i] * b_ary[j]
    }
  }
  ary[0..m]
end

def A010815(n)
  ary = [1]
  (1..n).each{|i|
    b_ary = Array.new(i + 1, 0)
    b_ary[0], b_ary[-1] = 1, -1
    ary = mul(ary, b_ary, n)
  }
  ary
end
ary = A010815(92)

# OEIS A010815のデータ
ary0 =
[1,-1,-1,0,0,1,0,1,0,0,0,0,-1,0,0,-1,0,0,0,0,0,0,
 1,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,
 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
 -1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]
# 一致の確認
p ary == ary0