OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
FORMULA
a(n) = Sum_{i=0..floor(n/2)} A255903(n-i,i).
EXAMPLE
a(4) = 5: {{1},{1},{1}}, {{1},{1,1}}, {{1,1,1}}, {{1},{2}}, {{1,2}}.
MAPLE
with(numtheory):
A:= proc(n, k) option remember; `if`(n=0, 1, add(A(n-j, k)*
add(d*binomial(d+k-1, k-1), d=divisors(j)), j=1..n)/n)
end:
T:= (n, k)-> add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k):
a:= n-> add(T(n-i, i), i=0..n/2):
seq(a(n), n=0..30);
MATHEMATICA
A[n_, k_] := A[n, k] = If[n==0, 1, Sum[A[n-j, k]*DivisorSum[j, #*Binomial[# +k-1, k-1]&], {j, 1, n}]/n];
T[n_, k_] := Sum[A[n, k-i]*(-1)^i*Binomial[k, i], {i, 0, k}];
a[n_] := Sum[T[n-i, i], {i, 0, n/2}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 24 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 30 2015
STATUS
approved