|
| |
|
|
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; 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.
|
|
|
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 * A102198 A100207 A172123
Adjacent sequences: A142959 A142960 A142961 * A142963 A142964 A142965
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Sep 15 2008
|
| |
|
|
