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EXAMPLE
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a(0) = 1: ( ).
a(1) = 1: (1).
a(2) = 2: (1,1), (1,2).
a(3) = 24: (1,1,1), (1,1,2), (1,1,3), (1,1,4), (1,1,5), (1,1,6), (1,1,7), (1,1,8), (1,1,9), (1,2,2), (1,2,3), (1,2,4), (1,2,5), (1,2,6), (1,2,7), (1,2,8), (1,2,9), (1,3,3), (1,3,4), (1,3,5), (1,3,6), (1,3,7), (1,3,8), (1,3,9).
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MAPLE
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b:= proc(n, k, i) option remember; `if`(n=0, 1,
add(b(n-1, k, j), j=1..min(i, k^(n-1))))
end:
a:= n-> b(n$2, infinity):
seq(a(n), n=0..6);
# second Maple program:
b:= proc(n, k) option remember; `if`(n=0, 1, -add(
b(j, k)*(-1)^(n-j)*binomial(k^j, n-j), j=0..n-1))
end:
a:= n-> b(n$2):
seq(a(n), n=0..12);
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