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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A142962 Scaled convolution of (n^3)*A000984(n) with A000984(n). A000984(n) = binomial(2*n,n) (central binomial coefficients). 1
4, 26, 81, 184, 350, 594, 931, 1376, 1944, 2650, 3509, 4536, 5746, 7154, 8775, 10624, 12716, 15066, 17689, 20600, 23814, 27346, 31211, 35424, 40000, 44954, 50301, 56056, 62234, 68850, 75919, 83456, 91476, 99994, 109025, 118584, 128686, 139346, 150579 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

S(3,n):= sum(p^3*binomial(2*p,p)*binomial(2*(n-p),n-p),p=0..n). a(n)=2^3*S(3,n)/4^n, n>=1. O.g.f. for S(3,n) is G(k=3,x). See triangle A142963 for the general G(k,x) formula.

The author was led to compute such sums by a question asked by M. Greiter, June 27, 2008.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n)=n^2*(3+5*n)/2. a(0):=0.

a(n)=(2^3)*S(3,n)/4^n with the convolution S(3,n) defined above.

O.g.f.: 2*x*(1+10*x+4*x^2)/(1-4*x)^4 (see triangle A142963 for the general G(k,x) formula).

CROSSREFS

A142962 triangle: row k=3: [3, 5], with the row polynomial 3+5*n.

Sequence in context: A099442 A014450 A200058 * A247194 A102198 A100207

Adjacent sequences:  A142959 A142960 A142961 * A142963 A142964 A142965

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang Sep 15 2008

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified December 18 02:13 EST 2014. Contains 252067 sequences.