|
| |
|
|
A211611
|
|
Sum_{k=1..n-1} C(k)^n, where C(k) is a Catalan number.
|
|
3
|
|
|
|
1, 9, 642, 540982, 5496576970, 698491214560174, 1147342896257677900291, 25005346993500437111980892595, 7381619397278667883874693730628586499, 30009934325456999669083059570156145437948880627, 1703283943023520710008632777768663744247664926649672215939
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
2,2
|
|
|
COMMENTS
|
The C(k) are the Catalan numbers, C(k) = A000108(k) = (2k)!/k!/(k+1)! = C(2*k,k)/(k+1).
p divides a(p) for prime p of the form p = 6k + 1.
|
|
|
LINKS
|
Table of n, a(n) for n=2..12.
Eric Weisstein's World of Mathematics, Catalan Number
|
|
|
FORMULA
|
a(n) = Sum[ (Binomial[2 k, k]/(k + 1))^n, {k, 1, n - 1}].
a(n) ~ exp(3/8) * 4^(n^2-n) / (Pi^(n/2) * n^(3*n/2)). - Vaclav Kotesovec, Mar 03 2014
|
|
|
MATHEMATICA
|
Table[ Sum[ (Binomial[2 k, k]/(k + 1))^n, {k, 1, n - 1}], {n, 2, 13}]
|
|
|
CROSSREFS
|
Cf. A000108, A211610, A238717.
Sequence in context: A158881 A188394 A157597 * A210053 A128795 A191510
Adjacent sequences: A211608 A211609 A211610 * A211612 A211613 A211614
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Alexander Adamchuk, Apr 17 2012
|
|
|
STATUS
|
approved
|
| |
|
|
