OFFSET
2,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..300
EXAMPLE
a(2) = 1: {a,a}.
a(3) = 3: {a,a,a}, {a,a,b}, {a,b,b}.
a(4) = 23: {a,a,a,a}, {a,a,aa}, {aa, aa}, {a,a,a,b}, {a,a,b,b}, {a,b,b,b}, {a,a,ab}, {a,a,ba}, {a,a,bb}, {b,b,ab}, {b,b,ba}, {b,b,aa}, {ab,ab}, {ba,ba}, {a,a,b,c}, {a,a,bc}, {a,a,cb}, {b,b,a,c}, {b,b,ac}, {b,b,ca}, {c,c,a,b}, {c,c,ab}, {c,c,ba}.
MAPLE
h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
end:
g:= proc(n, k) option remember; `if`(n=0, 1, add(add(
d*k^d, d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
end:
a:= n-> add(add((-1)^i*(g(n, k-i)-h(n$2, k-i))*
binomial(k, i), i=0..k), k=1..n-1):
seq(a(n), n=2..25);
MATHEMATICA
h[n_, i_, k_] := h[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[h[n - i*j, i - 1, k]*Binomial[k^i, j], {j, 0, n/i}]]];
g[n_, k_] := g[n, k] = If[n == 0, 1, Sum[Sum[d*k^d, {d, Divisors[j]}]*g[n - j, k], {j, 1, n}]/n];
T[n_, k_] := Sum[(-1)^i*(g[n, k-i]-h[n, n, k-i])*Binomial[k, i], {i, 0, k}];
a[n_] := Sum[T[n, k], {k, 1, n - 1}];
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 08 2018
STATUS
approved