|
| |
|
|
A000894
|
|
(2*n)!*(2*n+1)! /((n+1)! *n!^3).
|
|
4
|
|
|
|
1, 6, 60, 700, 8820, 116424, 1585584, 22084920, 312869700, 4491418360, 65166397296, 953799087696, 14062422446800, 208618354980000, 3111393751416000, 46619049708716400, 701342468412012900
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
a(n)=A001700*A000984 or a(n)=(A000984 n=0 to)*(A000984 n=1 to)/2. Example: 1,2,6,20,70,252,924,3432,12870... 2,6,20,70,252,924,3432,12870... 1*2/2=1 2*6/2=6 6*20/2=60 20*70/2=700 70*252/2=8 820 etc... - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 23 2007
|
|
|
REFERENCES
|
E. R. Hansen, A Table of Series and Products, Prentice-Hall, Englewood Cliffs, NJ, 1975, p. 96.
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..180
|
|
|
FORMULA
|
a(n)=C(2*n+1,n)*C(2*n,n), n>=0 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 23 2007
G.f.: (EllipticK(4*x^(1/2))-EllipticE(4*x^(1/2)))/(4*x*Pi). - Mark van Hoeij, Oct 24 2011
|
|
|
MAPLE
|
seq(binomial(2*n+1, n)*binomial(2*n, n), n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 23 2007
seq(binomial(2*n, n)/2*binomial(2*n-2, n-1), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 23 2007
|
|
|
PROG
|
(MAGMA) [Factorial(2*n)*Factorial(2*n+1) /(Factorial(n+1)* Factorial(n)^3): n in [0..20]]; // Vincenzo Librandi, Oct 25 2011
|
|
|
CROSSREFS
|
First differences of A082578. Cf. A002463.
Cf. A001700, A000984.
Sequence in context: A106259 A085364 A086984 * A112117 A065944 A126779
Adjacent sequences: A000891 A000892 A000893 * A000895 A000896 A000897
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
