OFFSET
0,3
COMMENTS
Inverse binomial transform of A000169.
It appears that a(n) is the number of partial functions f on [n] such that every point in [n] is either in the domain of f or in the image of f. Cf. A377763. - Geoffrey Critzer, Nov 06 2024
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..386
FORMULA
G.f.: Sum_{j>=1} A000169(j)*x^(j-1)/(1+x)^j. - Alois P. Heinz, Oct 31 2024
MAPLE
a:= n-> add((j+1)^j*(-1)^(n-j)*binomial(n, j), j=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, Oct 31 2024
MATHEMATICA
With[{t = Table[n^(n - 1), {n, 1, 21}]}, Table[Sum[(-1)^(i - j) * Binomial[i, j] * t[[j + 1]], {j, 0, i}], {i, 0, Length[t] - 1}]] (* Amiram Eldar, Oct 31 2024 *)
PROG
(PARI) lista(nn) = my(v = vector(nn+1, n, n^(n-1)), vv=vector(nn+1)); vv[1] = v[1]; for (n=1, nn, my(w = vector(#v-1, k, v[k+1] - v[k])); vv[n+1] = w[1]; v = w; ); vv; \\ Michel Marcus, Oct 31 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Harri Aaltonen, Oct 31 2024
STATUS
approved