OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..43
A. V. Sills and D. Zeilberger, Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz), arXiv:1108.4391 [math.CO], 2011.
FORMULA
a(n) = [x^(4^n-n*(n+1)/2)] Product_{j=1..n} 1/(1-x^j).
a(n) ~ 4^(n*(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015
EXAMPLE
a(2) = 7: 222222211, 2222221111, 22222111111, 222211111111, 2221111111111, 22111111111111, 211111111111111.
MATHEMATICA
maxExponent = 40; a[0] = 0; a[1] = 1;
a[n_] := Module[{}, aparts = List @@ (Product[1/(1 - x^j), {j, 1, n}] // Apart); cc = aparts + O[x]^maxExponent // CoefficientList[#, x]&; f[k_] = Total[FindSequenceFunction[#, k]& /@ cc]; f[4^n-n(n+1)/2 + 1] // Round];
Table[an = a[n]; Print[n, " ", an]; an, {n, 0, 11}] (* Jean-François Alcover, Nov 15 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 11 2014
STATUS
approved