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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A087804 Binomial transform of squares of Catalan numbers. 2
1, 2, 7, 41, 325, 3040, 31515, 350880, 4119125, 50381450, 636749395, 8266178915, 109733663665, 1484513264720, 20411163893039, 284613464884251, 4017787464584397, 57337159218724242, 826192231251644091, 12008313760729689717, 175899654887562881793, 2594832421996070470056, 38524582201629384371391 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: hypergeom([1/2, 1/2, 1], [2, 2], 16*x/(1-x))/(1-x).

E.g.f.: exp(x)*hypergeom([1/2, 1/2], [2, 2], 16*x).

-(n+1)^2*a(n)+(-15*n+4+19*n^2)*a(n-1)-(35*n-33)*(n-1)*a(n-2)+17*(n-1)*(n-2)*a(n-3) = 0. - Vladeta Jovovic, Jul 20 2004

a(n) ~ 17^(n+3)/(4096*Pi*n^3). - Vaclav Kotesovec, Oct 14 2012

MATHEMATICA

Table[Sum[Binomial[n, k]*(Binomial[2*k, k]/(k+1))^2, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)

PROG

(PARI) a(n)=sum(k=0, n, binomial(n, k)*(binomial(2*k, k)/(k+1))^2); \\ Joerg Arndt, May 10 2013

CROSSREFS

Cf. A007317, A001246.

Cf. A087806.

Sequence in context: A106871 A107376 A220896 * A006677 A101390 A113144

Adjacent sequences:  A087801 A087802 A087803 * A087805 A087806 A087807

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Oct 12 2003

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 23 05:13 EDT 2018. Contains 316519 sequences. (Running on oeis4.)