local bigint = require "pluto:bigint"
local fmt = require "fmt"
require "table2"

local branches = 4
local nmax = 250
local zero = bigint.new(0)
local one = bigint.new(1)
local rooted = table.rep(nmax, zero)
local unrooted = table.rep(nmax, zero)
local c = table.rep(branches, zero)

local function tree(br, n, l, sum, cnt)
    local b = br + 1
    while b <= branches do
        sum += n
        if sum > nmax then return end
        if l * 2 >= sum and b >= branches then return end
        if b == br + 1 then
            c[br + 1] = rooted[n] * cnt
        else
            local tmp = rooted[n] + bigint.new(b - br - 1)
            c[br + 1] *= tmp
            c[br + 1] /= bigint.new(b - br)
        end
        if l*2 < sum then unrooted[sum] += c[br + 1] end
        if b < branches then rooted[sum] += c[br + 1] end
        local m = n - 1
        while m > 0 do
            tree(b, m, l, sum, c[br + 1])
            m -= 1
        end
        b += 1
    end
end

local function bicenter(s)
    if s % 2 == 0 then
        local tmp = (rooted[s // 2] + one) * rooted[s // 2]
        tmp /= 2
        unrooted[s] += tmp
    end
end

rooted[1] = one
unrooted[1] = one
for n = 1, nmax do
    tree(0, n, n, 1, one)
    bicenter(n)
    fmt.print("%3d: %s", n, unrooted[n])
end