OFFSET
0,3
COMMENTS
a(n) is also the number of partitions of n^3 into n distinct parts <= n*(n+1). a(3) = 7: [4,11,12], [5,10,12], [6,9,12], [6,10,11], [7,8,12], [7,9,11], [8,9,10]. - Alois P. Heinz, Jan 25 2012
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..720 (terms 0..200 from Alois P. Heinz)
FORMULA
a(n) ~ c * d^n / n^2, where d = 5.4008719041181541524660911191042700520294... = A258234, c = 0.6326058791290010900659134913629203727... . - Vaclav Kotesovec, Sep 07 2014
MATHEMATICA
Table[Length[IntegerPartitions[n(n + 1)/2, n]], {n, 10}] (* Alonso del Arte, Aug 12 2011 *)
Table[SeriesCoefficient[Product[1/(1-x^k), {k, 1, n}], {x, 0, n*(n+1)/2}], {n, 0, 20}] (* Vaclav Kotesovec, May 25 2015 *)
PROG
(PARI)
a(n)=
{
local(tr=n*(n+1)/2, x='x+O('x^(tr+3)), gf);
gf = 1 / prod(k=1, n, 1-x^k); /* g.f. for partitions into parts <=n */
return( polcoeff( truncate(gf), tr ) );
} /* Joerg Arndt, Aug 14 2011 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 20 2010
EXTENSIONS
More terms from D. S. McNeil, Aug 12 2011
STATUS
approved