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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

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 | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 11 06:55 EST 2016. Contains 279043 sequences.