login
This site is supported by donations to The OEIS Foundation.

 

Logo

The submissions stack has been unacceptably high for several months now. Please voluntarily restrict your submissions and please help with the editing. (We don't want to have to impose further limits.)

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A065866 a(n) = n! * Catalan(n+1). 4
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)

0 = a(n)*(-7200*a(n+2) + 2700*a(n+3) + 246*a(n+4) - 33*a(n+5)) + a(n+1)*(+36*a(n+2) + 372*a(n+3) + 36*a(n+4) - a(n+5)) + a(n+2)*(-18*a(n+2) + 9*a(n+3) + a(n+4)) for n>=0. - Michael Somos, Apr 14 2015

The e.g.f. A(x) satisfies 0 = -2 + A(x) * (6*x - 2) + A'(x) * (4*x^2 - x). - Michael Somos, Apr 14 2015

EXAMPLE

G.f. = 1 + 2*x + 10*x^2 + 84*x^3 + 1008*x^4 + 15840*x^5 + 308880*x^6 + ...

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+1)/(i+1), i=0..18); # Zerinvary Lajos, Dec 16 2007

PROG

(PARI) { for (n = 0, 100, a = 2 * (2*n + 1)!/(n + 2)!; write("b065866.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 02 2009

CROSSREFS

Cf. A000108.

Equals 2 * A102693(n+1), n>0.

Main diagonal of A256116.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified August 29 04:48 EDT 2015. Contains 261184 sequences.