OFFSET
0,2
COMMENTS
Unordered partitions of n into parts where the part 1 comes in 4 colors. - Peter Bala, Dec 23 2013
From Omar E. Pol, Mar 01 2023: (Start)
Partial sums of A014153.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
From Peter Bala, Dec 23 2013: (Start)
O.g.f.: 1/(1 - x)^3 * Product_{k >= 1} 1/(1 - x^k).
a(n-1) + a(n-2) = Sum_{parts k in all partitions of n} J_2(k), where J_2(n) is the Jordan totient function A007434(n). (End)
a(n) ~ 3*sqrt(n) * exp(Pi*sqrt(2*n/3)) / (sqrt(2)*Pi^3). - Vaclav Kotesovec, Oct 30 2015
a(n) = Sum_{k=0..n} A014153(k). - Sean A. Irvine, Oct 14 2018
MATHEMATICA
nmax = 50; CoefficientList[Series[1/((1-x)^3 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 30 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved