|
|
A037966
|
|
a(n) = n^2*binomial(2*n-2, n-1).
|
|
9
|
|
|
0, 1, 8, 54, 320, 1750, 9072, 45276, 219648, 1042470, 4862000, 22355476, 101582208, 457002364, 2038517600, 9026235000, 39710085120, 173712232710, 756088415280, 3276123843300, 14138105520000, 60790319209620, 260516811228960, 1113068351807880, 4742456099097600, 20154752301937500, 85453569951920352
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
REFERENCES
|
The right-hand side of a binomial coefficient identity in H. W. Gould, Combinatorial Identities, Morgantown, 1972.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} k^2*binomial(n,k)^2. - Paul Barry, Mar 04 2003
(n-1)^3*a(n) = 2*n^2*(2*n-3)*a(n-1). - R. J. Mathar, Jul 26 2015
E.g.f.: x*exp(2*x)*((1 + 2*x)*BesselI(0,2*x) + 2*x*BesselI(1,2*x)). - Ilya Gutkovskiy, Mar 04 2021
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) [0] cat [n^3*Catalan(n-1): n in [1..30]]; // G. C. Greubel, Jun 19 2022
(SageMath) [n^3*catalan_number(n-1) for n in (0..30)] # G. C. Greubel, Jun 19 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|