OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..380
FORMULA
a(n) = A079025(2n,n).
EXAMPLE
a(2) = 16: The partitions of 2*2 are (4), (31), (22), (211), (1111). Least numbers with these prime signatures are 16, 24, 36, 60, 210. Their divisors with prime signatures (2) or (11) are {4}, {4,6}, {4,6,9}, {4,6,10,15}, {6,10,14,15,21,35}. The total number is 1 + 2 + 3 + 4 + 6.
MAPLE
b:= proc(n, i) option remember; expand(`if`(n=0 or i=1, (x+1)^n,
b(n, i-1) +factor((x^(i+1)-1)/(x-1))*b(n-i, min(n-i, i))))
end:
a:= n-> coeff(b(2*n$2), x, n):
seq(a(n), n=0..25);
MATHEMATICA
b[n_, i_] := b[n, i] = Expand[If[n == 0 || i == 1, (x + 1)^n, b[n, i - 1] + Factor[(x^(i + 1) - 1)/(x - 1)] b[n - i, Min[n - i, i]]]];
a[n_] := Coefficient[b[2n, 2n], x, n];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 22 2019
STATUS
approved