Faulhaber's triangle: Difference between revisions
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faulhaber(4, 1000)
200500333333300</pre>
=={{header|Julia}}==
<lang julia>function bernoulli(n)
A = Vector{Rational{BigInt}}(undef, n + 1)
for i in 0:n
A[i + 1] = 1 // (i + 1)
for j = i:-1:1
A[j] = j * (A[j] - A[j + 1])
end
end
return n == 1 ? -A[1] : A[1]
end
function faulhabercoeffs(p)
coeffs = Vector{Rational{BigInt}}(undef, p + 1)
q = Rational{BigInt}(1, p + 1)
sign = -1
for j in 0:p
sign *= -1
coeffs[p - j + 1] = bernoulli(j) * (q * sign) * Rational{BigInt}(binomial(p + 1, j), 1)
end
coeffs
end
faulhabersum(n, k) = begin coe = faulhabercoeffs(k); mapreduce(i -> BigInt(n)^i * coe[i], +, 1:k+1) end
prettyfrac(x) = (x.num == 0 ? "0" : x.den == 1 ? string(x.num) : replace(string(x), "//" => "/"))
function testfaulhaber()
for i in 0:9
for c in faulhabercoeffs(i)
print(prettyfrac(c), "\t")
end
println()
end
println("\n", prettyfrac(faulhabersum(1000, 17)))
end
testfaulhaber()
</lang>{{out}}
<pre>
1
1/2 1/2
1/6 1/2 1/3
0 1/4 1/2 1/4
-1/30 0 1/3 1/2 1/5
0 -1/12 0 5/12 1/2 1/6
1/42 0 -1/6 0 1/2 1/2 1/7
0 1/12 0 -7/24 0 7/12 1/2 1/8
-1/30 0 2/9 0 -7/15 0 2/3 1/2 1/9
0 -3/20 0 1/2 0 -7/10 0 3/4 1/2 1/10
56056972216555580111030077961944183400198333273050000
</pre>
=={{header|Kotlin}}==
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