Template:Gender of Boolean functions/triangles/total

total

This triangle shows the numbers of Boolean functions with arity $n$ and valency $k$. The right diagonal is ${\boldsymbol {p}}$ =  A000371. ${\boldsymbol {p}}(n)$ is the number of non-degenerate $n$-ary Boolean functions. (See root.) This is Pascal's triangle with column $k$ multiplied by ${\boldsymbol {p}}(k)$. The sum of row $n$ is $2^{2^{n}}$.   ( A001146) k n 0 1 2 3 4 5 sums 0 1 · 2 2 2 1 1 · 2 2 1 · 2 2 4 2 1 · 2 2 2 · 2 4 1 · 10 10 16 3 1 · 2 2 3 · 2 6 3 · 10 30 1 · 218 218 256 4 1 · 2 2 4 · 2 8 6 · 10 60 4 · 218 872 1 · 64594 64594 65536 5 1 · 2 2 5 · 2 10 10 · 10 100 10 · 218 2180 5 · 64594 322970 1 · 4294642034 4294642034 4294967296