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Linear recursion with Catalan numbers.
1

%I #11 Sep 08 2022 08:45:00

%S 2,9,32,115,420,1554,5808,21879,82940,316030,1209312,4644094,17889032,

%T 69089700,267444000,1037348415,4030774380,15687019590,61137753600,

%U 238580530650,932105099640,3645473785980,14271279927840,55918717024950,219283705045080,860564513057004,3379592965275968

%N Linear recursion with Catalan numbers.

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

%H G. C. Greubel, <a href="/A053369/b053369.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = (7n+2)*C(n) where C(n)=Catalan numbers (A000108).

%t Table[(7*n + 2)*CatalanNumber[n], {n, 0, 50}] (* _G. C. Greubel_, May 25 2018 *)

%o (PARI) for(n=0,30, print1(((7*n+2)/(n+1))*binomial(2*n,n), ", ")) \\ _G. C. Greubel_, May 25 2018

%o (Magma) [((7*n+2)/(n+1))*Binomial(2*n,n): n in [0..30]]; // _G. C. Greubel_, May 25 2018

%Y Cf. A050960.

%K easy,nonn

%O 0,1

%A _Barry E. Williams_, Jan 06 2000

%E Terms a(21) onward added by _G. C. Greubel_, May 25 2018