OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..2000
FORMULA
G.f.: 1/Product(1-b(n)*x^n, n=1..infinity), where b(n) is sum of number of partitions of parts in all partitions of n; b() is convolution of A047968() and A000041(). - Vladeta Jovovic, Nov 22 2005
From Vaclav Kotesovec, Mar 28 2016: (Start)
a(n) ~ c * 21^(n/4), where
c = 31506.382471540934704971753670563958673161001663... if mod(n,4) = 0
c = 31502.248225846169487427060315658509213347537914... if mod(n,4) = 1
c = 31506.175349116205868096360427802563935891182649... if mod(n,4) = 2
c = 31502.232274793501377850265964413938565498517297... if mod(n,4) = 3
(End)
MATHEMATICA
Table[Plus@@((Apply[Plus, #/. i_Integer-> PartitionsP[i], {1}]/. f->Times)& /@ Flatten[Flatten[Outer[f, Sequence@@(Partitions/@#), 1]]&/@Partitions[w]]), {w, 16}]
nmax = 40; A047968 = Table[Sum[PartitionsP[d], {d, Divisors[n]}], {n, 1, nmax}]; conv = Table[Sum[A047968[[j]]*PartitionsP[m - j], {j, 1, m}], {m, 1, nmax}]; A063835 = Rest[CoefficientList[Series[Product[1/(1 - conv[[k]]*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Mar 27 2016 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Wouter Meeussen, Aug 21 2001
EXTENSIONS
More terms from Vladeta Jovovic, Nov 22 2005
STATUS
approved