OFFSET
0,10
COMMENTS
a(n) is the number of compositions of n such that the first part is equal to the number of parts and all parts are greater than or equal to the first part. - John Tyler Rascoe, Feb 10 2024
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Sum_{k>=0} x^((k+1)^2)/(1-x)^k.
G.f.: Sum_{k>0} A(x,k) where A(x,k) = (x^k)*(x^k/(1-x))^(k-1) is the g.f. for compositions of this kind with first part k. - John Tyler Rascoe, Feb 10 2024
EXAMPLE
From John Tyler Rascoe, Feb 10 2024: (Start)
The compositions for n = 9..11 are:
9: [3,3,3], [2,7];
10: [3,4,3], [3,3,4], [2,8];
11: [3,4,4], [3,3,5], [3,5,3], [2,9].
(End)
PROG
(PARI) N=66; q='q+O('q^N);
gf=sum(n=0, N, q^((n+1)^2) / (1-q)^n );
concat([0], Vec(gf))
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Apr 22 2014
STATUS
approved