OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..8000
FORMULA
G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*d(j)^k*x^(j*k)/k), where d(j) is the number of the divisors of j (A000005). - Ilya Gutkovskiy, Jul 17 2018
EXAMPLE
The a(5)=9 twice-partitions are:
((5)), ((4)(1)), ((3)(2)), ((3)(11)), ((22)(1)),
((111)(2)), ((111)(11)), ((1111)(1)), ((11111)).
MAPLE
b:= proc(n, i) option remember;
`if`(n>i*(i+1)/2, 0, `if`(n=0, 1, b(n, i-1)+
`if`(i>n, 0, numtheory[tau](i)*b(n-i, i-1))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..70); # Alois P. Heinz, Dec 20 2016
MATHEMATICA
nn=20; CoefficientList[Series[Product[(1+DivisorSigma[0, n]x^n), {n, nn}], {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 18 2016
STATUS
approved