login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111997 Ninth convolution of Schroeder's (second problem) numbers A001003(n), n>=0. 1
1, 9, 63, 399, 2403, 14067, 80949, 460845, 2605590, 14666470, 82320714, 461238282, 2581644378, 14442658074, 80785970838, 451934259654, 2528977211775, 14157983986839, 79302044283297, 444448115168049, 2492468172937125 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: ((1+x-sqrt(1-6*x+x^2))/(4*x))^9.
a(n) = (9/n)*Sum_{k=1,..,n} binomial(n,k)*binomial(n+k+8,k-1).
a(n) = 9*hypergeom([1-n, n+10], [2], -1), n>=1, a(0)=1.
Recurrence: n*(n+9)*a(n) = (7*n^2+51*n+32)*a(n-1) - (7*n^2+33*n-22)*a(n-2) + (n-3)*(n+6)*a(n-3). - Vaclav Kotesovec, Oct 18 2012
a(n) ~ 9*sqrt(3*sqrt(2)-4)*(577-408*sqrt(2)) * (3+2*sqrt(2))^(n+9)/(64*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 18 2012
MATHEMATICA
CoefficientList[Series[((1+x-Sqrt[1-6*x+x^2])/(4*x))^9, {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 18 2012 *)
PROG
(PARI) x='x+O('x^50); Vec(((1+x-sqrt(1-6*x+x^2))/(4*x))^9) \\ G. C. Greubel, Mar 17 2017
CROSSREFS
Ninth column of convolution triangle A011117.
Sequence in context: A073378 A316461 A022733 * A016137 A230547 A339786
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 12 2005
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)