%I #16 Jan 05 2024 21:14:11

%S 1,5,12,38,130,462,1680,6204,23166,87230,330616,1259700,4820452,

%T 18513068,71318400,275467320,1066432950,4136847390,16075953960,

%U 62570669700,243882320220,951797460900,3718872587040,14545727618760

%N Central elements in the 5-Pascal triangle A028313.

%H G. C. Greubel, <a href="/A028322/b028322.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (1 + 3*x)/sqrt(1-4*x). - _Vladeta Jovovic_, Jan 08 2004

%F a(n) = A000984(n) + 3*A000984(n-1). - _R. J. Mathar_, Dec 15 2015

%F a(n) = (n+1)*(7*n-2)*A000108(n)/(2*(2*n-1)). - _G. C. Greubel_, Jan 05 2024

%t Table[(n+1)*(7*n-2)*CatalanNumber[n]/(2*(2*n-1)), {n,0,40}] (* _G. C. Greubel_, Jan 05 2024 *)

%o (Magma) [(n+1)*(7*n-2)*Catalan(n)/(2*(2*n-1)): n in [0..40]]; // _G. C. Greubel_, Jan 05 2024

%o (SageMath) [(7*n-2)*binomial(2*n,n)/(2*(2*n-1)) for n in range(41)] # _G. C. Greubel_, Jan 05 2024

%Y Cf. A000108, A000984, A028313.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_

%E More terms from _James A. Sellers_