OFFSET
0,3
COMMENTS
a(n) = < PF_n, PF_n >, where PF_n is the parking function symmetric function and <,> denotes the usual scalar product on symmetric functions (proved). - Richard Stanley, Sep 24 2015
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..339
FORMULA
a(n) = [x^n] 1/(1-x)^((n+1)^2) / (n+1)^2 ; that is, a(n) equals the coefficient of x^n in 1/(1-x)^((n+1)^2) divided by (n+1)^2.
MAPLE
A182316:=n->binomial(n^2 + 3*n, n) / (n+1)^2: seq(A182316(n), n=0..20); # Wesley Ivan Hurt, Feb 11 2017
PROG
(PARI) {a(n)=binomial((n+1)^2+n-1, n)/(n+1)^2}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul D. Hanna, Apr 24 2012
STATUS
approved