OFFSET
1,2
COMMENTS
Partial sum operator applied to partition numbers 4 times.
FORMULA
a(n) = ((n+1)*(n+2)*(A000070(n)-1) - (2*n+3)*A182738(n) + A259279(n))/2. - Vaclav Kotesovec, Jun 23 2015
a(n) ~ 3*sqrt(n) * exp(Pi*sqrt(2*n/3)) / (sqrt(2)*Pi^3). - Vaclav Kotesovec, Jun 23 2015
MATHEMATICA
s1=s2=s3=0; lst={}; Do[AppendTo[lst, s3+=s2+=s1+=PartitionsP[n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 16 2009 *)
Table[Sum[PartitionsP[k]*(n-k+1)*(n-k+2)/2, {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, Jun 23 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Perry, Jul 29 2003
STATUS
approved