login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182316 a(n) = binomial(n^2 + 3*n, n) / (n+1)^2. 2
1, 1, 5, 51, 819, 18278, 527085, 18730855, 793542167, 39113958819, 2201663313200, 139461523272085, 9824294829146550, 762188806010669820, 64595315110014533629, 5939055918736259991759, 588894813538193130767295, 62651281502108852275337225 (list; graph; refs; listen; history; text; internal format)
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

Cf. A143669.

Sequence in context: A234290 A107669 A218675 * A077392 A193444 A243242

Adjacent sequences:  A182313 A182314 A182315 * A182317 A182318 A182319

KEYWORD

nonn,easy

AUTHOR

Paul D. Hanna, Apr 24 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)