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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A360083 a(n) = Sum_{k=0..n} binomial(5*k,n-k) * Catalan(k). 3
 1, 1, 7, 35, 189, 1092, 6538, 40278, 253730, 1626858, 10582616, 69669273, 463319257, 3107941405, 21004392887, 142882885210, 977562617826, 6722361860888, 46438235933700, 322111000796428, 2242538435656450, 15665017062799230, 109761527468995102 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..22. FORMULA G.f. A(x) satisfies A(x) = 1/(1 - x * (1+x)^5 * A(x)). G.f.: 2 / (1 + sqrt( 1 - 4*x*(1+x)^5 )). PROG (PARI) a(n) = sum(k=0, n, binomial(5*k, n-k)*binomial(2*k, k)/(k+1)); (PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x*(1+x)^5))) CROSSREFS Cf. A052709, A073155, A360076, A360082. Cf. A000108, A360090. Sequence in context: A026128 A026157 A025184 * A267712 A263513 A274073 Adjacent sequences: A360080 A360081 A360082 * A360084 A360085 A360086 KEYWORD nonn 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.

Last modified August 7 08:03 EDT 2024. Contains 375008 sequences. (Running on oeis4.)