Faulhaber's formula: Difference between revisions
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8 : 1/9n^9 + 1/2n^8 + 2/3n^7 - 7/15n^5 + 2/9n^3 - 1/30n
9 : 1/10n^10 + 1/2n^9 + 3/4n^8 - 7/10n^6 + 1/2n^4 - 3/20n^2</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<lang Mathematica>ClearAll[Faulhaber]
Faulhaber[n_, 0] := n
Faulhaber[n_, p_] := n^(p + 1)/(p + 1) + 1/2 n^p + Sum[BernoulliB[k]/k! p!/(p - k + 1)! n^(p - k + 1), {k, 2, p}]
Table[{p, Faulhaber[n, p]}, {p, 0, 9}] // Grid</lang>
{{out}}
<pre>0 n
1 n/2+n^2/2
2 n/6+n^2/2+n^3/3
3 n^2/4+n^3/2+n^4/4
4 -(n/30)+n^3/3+n^4/2+n^5/5
5 -(n^2/12)+(5 n^4)/12+n^5/2+n^6/6
6 n/42-n^3/6+n^5/2+n^6/2+n^7/7
7 n^2/12-(7 n^4)/24+(7 n^6)/12+n^7/2+n^8/8
8 -(n/30)+(2 n^3)/9-(7 n^5)/15+(2 n^7)/3+n^8/2+n^9/9
9 -((3 n^2)/20)+n^4/2-(7 n^6)/10+(3 n^8)/4+n^9/2+n^10/10</pre>
=={{header|Maxima}}==
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