A182316 a(n) = binomial(n^2 + 3*n, n) / (n+1)^2.

1, 1, 5, 51, 819, 18278, 527085, 18730855, 793542167, 39113958819, 2201663313200, 139461523272085, 9824294829146550, 762188806010669820, 64595315110014533629, 5939055918736259991759, 588894813538193130767295, 62651281502108852275337225

Offset: 0

Author

Paul D. Hanna, Apr 24 2012

Keywords

• nonn
• easy

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

Crossrefs

Cf. A143669.

Programs

Maple

A182316:=n->binomial(n^2 + 3*n, n) / (n+1)^2: seq(A182316(n), n=0..20); # Wesley Ivan Hurt, Feb 11 2017

PARI

{a(n)=binomial((n+1)^2+n-1, n)/(n+1)^2}
for(n=0,20,print1(a(n),","))

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.