OFFSET
1,6
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Wikipedia, Elementary symmetric polynomial
EXAMPLE
a(2) = 2 counts {1,11}, {1,2,3}.
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 - 1]}]]; 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-1), 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
Terms a(35) and beyond from Andrew Howroyd, Dec 17 2018
STATUS
approved