OFFSET
2,2
FORMULA
a(n) = binomial(2*n-2,n) - (n-1) = A001791(n-1) -n+1.
G.f.: 4*x^2/((1 - sqrt(1 - 4*x))^2*sqrt(1 - 4*x)) - (1 - 2*x + 2*x^2)/(1 - x)^2. - Stefano Spezia, Jan 10 2022
D-finite with recurrence +n*(11*n-38)*a(n) -(n-1)*(73*n-244)*a(n-1) +2*(67*n^2-364*n+492)*a(n-2) -4*(9*n-22)*(2*n-7)*a(n-3)=0. - R. J. Mathar, Mar 06 2022
EXAMPLE
a(5)=52 since 5 can be written as 5+0+0+0 (4 such compositions); 4+1+0+0 (12 such compositions); 3+2+0+0 (12 such compositions); 3+1+1+0 (12 such compositions); 2+2+1+0 (12 such compositions). All these weak compositions contain at least one zero.
MATHEMATICA
a[n_] := Binomial[2*n - 2, n] - n + 1; Array[a, 25, 2] (* Amiram Eldar, Jan 10 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Jan 09 2022
STATUS
approved