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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144186 Numerators of series expansion of the e.g.f. for the Catalan numbers. 6
1, 1, 1, 5, 7, 7, 11, 143, 143, 2431, 4199, 4199, 7429, 7429, 7429, 215441, 392863, 392863, 20677, 765049, 765049, 31367009, 58642669, 58642669, 2756205443, 2756205443, 2756205443, 146078888479, 5037203051, 5037203051, 9586934839 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..30.

Eric Weisstein's World of Mathematics, Catalan Number

FORMULA

The e.g.f. is Sum_{n >= 0} (x^n/n!)*binomial(2n,n)/(n+1).

EXAMPLE

E^(2*x)*(BesselI[0, 2*x] - BesselI[1, 2*x]) = 1 + x + x^2 + (5*x^3)/6 + (7*x^4)/12 + ...

The coefficients continue like this: 1, 1, 1, 5/6, 7/12, 7/20, 11/60, 143/1680, 143/4032, 2431/181440, 4199/907200, 4199/2851200, 7429/17107200, 7429/62270208, ...

MAPLE

seq(numer(binomial(2*n, n)/(n+1)!), n=0..30); # Vladeta Jovovic, Dec 03 2008

CROSSREFS

Cf. A000108, A144187.

Sequence in context: A231935 A216835 A033932 * A246458 A153979 A126992

Adjacent sequences:  A144183 A144184 A144185 * A144187 A144188 A144189

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Sep 13 2008

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 18:10 EDT 2018. Contains 316323 sequences. (Running on oeis4.)