OFFSET
0,2
COMMENTS
Number of ways to pick n units in all partitions of 2n - Olivier Gérard, May 07 2020
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1663 (first 301 terms from Vaclav Kotesovec)
FORMULA
a(n) ~ c * 4^n / sqrt(Pi*n), where c = 1/(2*QPochhammer[1/2, 1/2]) = 1.7313733097275318057689... - Vaclav Kotesovec, Sep 20 2017
a(n) = A292508(n,n+1). - Alois P. Heinz, Jul 16 2021
EXAMPLE
Illustration of comment for n=3, a(3)=25 :
Among the 11 integer partitions of 6, 3 have at least 3 ones.
3,1,1,1 ; 2,1,1,1,1; 1,1,1,1,1,1;
There are respectively 1, 4 and 20 ways to pick 3 of these.
MATHEMATICA
Table[SeriesCoefficient[1/(1-x)^n*Product[1/(1-x^k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 20 2017
STATUS
approved