login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A277969 a(n) = Sum_{k=0..n} binomial(n-3,n-k)*Catalan(k). 1
1, -1, 2, 5, 19, 75, 305, 1270, 5390, 23236, 101480, 448085, 1997115, 8973255, 40602093, 184853055, 846206025, 3892585325, 17984308775, 83417287855, 388297304825, 1813341109825, 8493372326675, 39889629750600, 187812852106636 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Robert Israel, Table of n, a(n) for n = 0..1430

FORMULA

G.f.: ((1-x)^3*(1-sqrt((5*x-1)/(x-1))))/(2*x).

a(n) ~ 8*5^(n-3/2) / (sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Nov 07 2016

(5*n-10)*a(n)-(7+6*n)*a(n+1)+(n+3)*a(n+2)=0 for n >= 2. - Robert Israel, Nov 21 2016

a(n) = A055452(n+1) for n > 2. - Georg Fischer, Oct 23 2018

MAPLE

f:= gfun:-rectoproc({(5*n-10)*a(n)+(-7-6*n)*a(n+1)+(n+3)*a(n+2), a(0) = 1, a(1) = -1, a(2) = 2, a(3) = 5}, a(n), remember):

map(f, [$0..30]); # Robert Israel, Nov 21 2016

MATHEMATICA

CoefficientList[Series[((1 - x)^3 (1 - Sqrt[(5 x - 1) / (x - 1)])) / (2 x), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 07 2016 *)

PROG

(Maxima)

a(n):=sum((binomial(2*k, k)*binomial(n-3, n-k))/(k+1), k, 0, n);

(PARI) x='x+O('x^50); Vec(((1-x)^3*(1-sqrt((5*x-1)/(x-1))))/(2*x)) \\ G. C. Greubel, Apr 09 2017

CROSSREFS

Cf. A000108, A055452.

Sequence in context: A255541 A150026 A150027 * A058131 A222055 A228569

Adjacent sequences:  A277966 A277967 A277968 * A277970 A277971 A277972

KEYWORD

sign

AUTHOR

Vladimir Kruchinin, Nov 06 2016

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 02:45 EST 2020. Contains 338756 sequences. (Running on oeis4.)