OFFSET
1,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1001 terms from Antti Karttunen)
FORMULA
a(1) = 0; a(n+1) = Sum_{d|n} binomial(n/d+a(d)-2,a(d)-1).
MAPLE
a:= proc(n) option remember; uses numtheory;
add(binomial((n-1)/d+a(d)-2, a(d)-1), d=divisors(n-1))
end:
seq(a(n), n=1..80); # Alois P. Heinz, Jan 27 2025
MATHEMATICA
a[n_] := a[n] = SeriesCoefficient[x Sum[x^k/(1 - x^k)^a[k], {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 80}]
a[n_] := a[n] = Sum[Binomial[(n - 1)/d + a[d] - 2, a[d] - 1], {d, Divisors[n - 1]}]; a[1] = 0; Table[a[n], {n, 1, 80}]
PROG
(PARI) seq(n)={my(v=vector(n)); v[2]=1; for(n=2, #v-1, v[n+1] = sumdiv(n, d, binomial(n/d + v[d] - 2, v[d] - 1))); v} \\ Andrew Howroyd, Aug 10 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 10 2019
STATUS
approved