160719(2)

Ruby

Triangular array associated with Schroeder numbers

オンライン整数列大辞典の

A033877（http://oeis.org/A033877/list）
に載っているが、自分でも求めてみた。

n = 20
# 1行目
a = [0, 1]
n.times{|i|
  a << 0
  b = [0]
  (0..i).each{|j| b[j + 1] = a[j] + a[j + 1] + b[j]}
  a = b
  p [i + 1, a[1..-1]]
}

出力結果
[1, [1]]
[2, [1, 2]]
[3, [1, 4, 6]]
[4, [1, 6, 16, 22]]
[5, [1, 8, 30, 68, 90]]
[6, [1, 10, 48, 146, 304, 394]]
[7, [1, 12, 70, 264, 714, 1412, 1806]]
[8, [1, 14, 96, 430, 1408, 3534, 6752, 8558]]
[9, [1, 16, 126, 652, 2490, 7432, 17718, 33028, 41586]]
[10, [1, 18, 160, 938, 4080, 14002, 39152, 89898, 164512, 206098]]
[11, [1, 20, 198, 1296, 6314, 24396, 77550, 206600, 461010, 831620, 1037718]]
[12, [1, 22, 240, 1734, 9344, 40054, 142000, 426150, 1093760, 2386390, 4255728, 5293446]]
[13, [1, 24, 286, 2260, 13338, 62736, 244790, 812940, 2332850, 5813000, 12455118, 22004292, 27297738]]
[14, [1, 26, 336, 2882, 18480, 94554, 402080, 1459810, 4605600, 12751450, 31019568, 65478978, 114781008, 142078746]]
[15, [1, 28, 390, 3608, 24970, 138004, 634638, 2496528, 8561938, 25918988, 69690006, 166188552, 346448538, 603308292, 745387038]]
[16, [1, 30, 448, 4446, 33024, 195998, 968640, 4099806, 15158272, 49639198, 145248192, 381126750, 893763840, 1843520670, 3192216000, 3937603038]]
[17, [1, 32, 510, 5404, 42874, 271896, 1436534, 6504980, 25763058, 90560528, 285447918, 811822860, 2086713450, 4823997960, 9859734630, 16989553668, 20927156706]]
[18, [1, 34, 576, 6490, 54768, 369538, 2077968, 10019482, 42287520, 158611106, 534619552, 1631890330, 4530426640, 11441138050, 26124870640, 52974158938, 90890869312, 111818026018]]
[19, [1, 36, 646, 7712, 68970, 493276, 2940782, 15038232, 67345234, 268243860, 961474518, 3127984400, 9290301370, 25261866060, 62827874750, 141926904328, 285791932578, 488500827908, 600318853926]]
[20, [1, 38, 720, 9078, 85760, 648006, 4082064, 22061078, 104444544, 440033638, 1669752016, 5759210934, 18177496704, 52729664134, 140819404944, 345574184022, 773293020928, 1547585781414, 2636405463248, 3236724317174]]