|
| |
|
|
A065866
|
|
n!* Catalan(n+1).
|
|
3
|
|
|
|
1, 2, 10, 84, 1008, 15840, 308880, 7207200, 196035840, 6094932480, 213322636800, 8303173401600, 355850288640000, 16653793508352000, 845180020548864000, 46236318771202560000, 2712530701243883520000, 169890080762116915200000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
R. L. Graham, D. E. Knuth, O. Patashnik, "Concrete Mathematics", Addison-Wesley, 1994, pp. 200-204.
|
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=0,...,100
|
|
|
FORMULA
|
a(n) = 2 * (2n+1)!/(n+2)!. E.g.f.: (1-2x-sqrt(1-4x))/(2x^2) = (O.g.f. for A000108)^2 = B_2(x)^2 (cf. GKP reference)
|
|
|
MAPLE
|
with(combstruct):ZL:=[T, {T=Union(Z, Prod(Epsilon, Z, T), Prod(T, Z, Epsilon), Prod(T, T, Z))}, labeled]:seq(count(ZL, size=i)/i, i=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2007
|
|
|
PROG
|
(PARI) { for (n = 0, 100, a = 2 * (2*n + 1)!/(n + 2)!; write("b065866.txt", n, " ", a) ) } [From Harry J. Smith, Nov 02 2009]
|
|
|
CROSSREFS
|
Cf. A000108.
Equals 2 * A102693(n+1), n>0.
Sequence in context: A113332 A180715 A107863 * A156466 A132397 A202745
Adjacent sequences: A065863 A065864 A065865 * A065867 A065868 A065869
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 06 2001
|
|
|
STATUS
|
approved
|
| |
|
|
