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%I #21 Jul 08 2023 04:02:42
%S 2,7,24,85,308,1134,4224,15873,60060,228514,873392,3350802,12896744,
%T 49774300,192559680,746503065,2899328940,11279096730,43942760400,
%U 171424529430,669540282840,2617890571140,10246047127680,40137974797050,157368305973528,617467192984404,2424490605524064
%N a(n) = (5n+2)*C(n) where C(n) = Catalan numbers (A000108).
%D Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H G. C. Greubel, <a href="/A053368/b053368.txt">Table of n, a(n) for n = 0..1000</a>
%F From _R. J. Mathar_, Feb 13 2015: (Start)
%F 3*(n+1)*a(n) + 2*(-7*n-2)*a(n-1) + 4*(2*n-3)*a(n-2) = 0.
%F -(n+1)*(5*n-3)*a(n) + 2*(5*n+2)*(2*n-1)*a(n-1) = 0. (End)
%F G.f.: (3 - 2*x - 3*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - _Amiram Eldar_, Jul 08 2023
%t Table[(5*n + 2)*CatalanNumber[n], {n, 0, 50}] (* _G. C. Greubel_, May 25 2018 *)
%o (PARI) for(n=0,30, print1(((5*n+2)/(n+1))*binomial(2*n,n), ", ")) \\ _G. C. Greubel_, May 25 2018
%o (Magma) [((5*n+2)/(n+1))*Binomial(2*n,n): n in [0..30]]; // _G. C. Greubel_, May 25 2018
%Y Cf. A000108, 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
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