OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Wikipedia, Elementary symmetric polynomial
EXAMPLE
a(9) = 4 counts {1,9}, {3,3}, {1,1,4}, {1,1,1,2}.
a(33) = 10 counts {1,1,1,1,1,1,3}, {1,1,1,2,2,2}, {1,1,1,10}, {1,1,2,7}, {1,1,4,4}, {1,1,16}, {1,2,2,5}, {1,33}, {3,3,4}, {3,11}.
MATHEMATICA
a[n_] := Module[{r}, r[lim_, s1_, s2_] := r[lim, s1, s2] = If[s2 == n, 1, Sum[r[i, s1 + i, s2 + s1 i], {i, 1, Min[Quotient[n - s2, s1], lim]}]]; Sum[r[i, i, 0], {i, 1, n}]];
a /@ Range[1, 100] (* Jean-François Alcover, Sep 28 2019, after Andrew Howroyd *)
PROG
(PARI) a(n)={my(recurse(lim, s1, s2)=if(s2==n, 1, sum(i=1, min((n-s2)\s1, lim), self()(i, s1+i, s2+s1*i)))); sum(i=1, n, recurse(i, i, 0))} \\ Andrew Howroyd, Dec 17 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(33) corrected by Laurance L. Y. Lau, Dec 17 2018
Terms a(35) and beyond from Andrew Howroyd, Dec 17 2018
STATUS
approved