OFFSET
1,3
COMMENTS
Number of ways to write n as an orderless product of orderless sums with distinct factors and each sum composed of distinct parts. Compare A318949.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
EXAMPLE
The a(4) = 2 ways: (4), (3+1).
The a(6) = 6 ways: (6), (4+2), (5+1), (3+2+1), (2)*(3), (2)*(2+1).
PROG
(PARI)
MultWeighT(u)={my(n=#u, v=vector(n, k, k==1)); for(k=2, n, if(u[k], my(m=logint(n, k), p=(1 + x + O(x*x^m))^u[k], w=vector(n)); for(i=0, m, w[k^i]=polcoef(p, i)); v=dirmul(v, w))); v}
seq(n)={MultWeighT(Vec(eta(x^2 + O(x*x^n))/eta(x + O(x*x^n)) - 1))} \\ Andrew Howroyd, Oct 27 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 26 2019
STATUS
approved