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!)
A360084 a(n) = Sum_{k=0..n} (-1)^k * binomial(3*k,n-k) * Catalan(k). 2
1, -1, -1, 4, -2, -14, 36, -1, -191, 418, 182, -2904, 5546, 5226, -47466, 78843, 121489, -813060, 1157400, 2659695, -14364997, 17078752, 56866292, -259091498, 246553176, 1202210486, -4736784794, 3346401868, 25255328948, -87323306720, 39123129700 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
G.f. A(x) satisfies A(x) = 1/(1 + x * (1+x)^3 * A(x)).
G.f.: 2 / (1 + sqrt( 1 + 4*x*(1+x)^3 )).
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(3*k, n-k)*binomial(2*k, k)/(k+1));
(PARI) my(N=40, x='x+O('x^N)); Vec(2/(1+sqrt(1+4*x*(1+x)^3)))
CROSSREFS
Cf. A000108.
Sequence in context: A317738 A224893 A087957 * A019061 A019012 A154333
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jan 25 2023
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 April 14 20:39 EDT 2024. Contains 371667 sequences. (Running on oeis4.)