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A113894 a(n) = binomial(2*n, n) * binomial(2*n+5, n).

%I A113894 #11 Mar 02 2025 08:00:49
%S A113894 1,14,216,3300,50050,756756,11435424,172931616,2618916300,39731777800,
%T A113894 603923022560,9197348345640,140334704005860,2145155731845000,
%U A113894 32847841152720000,503812888080163200,7739375660195721300,119063197872768778200,1834199559285273180000
%N A113894 a(n) = binomial(2*n, n) * binomial(2*n+5, n).
%H A113894 Andrew Howroyd, <a href="/A113894/b113894.txt">Table of n, a(n) for n = 0..200</a>
%F A113894 a(n) = A062190(2*n, n).
%e A113894 a(0) = C(0,0)*C(5,0) = 1*1 = 1.
%e A113894 a(4) = C(8,4)*C(13,4) = 70*715 = 50050.
%e A113894 a(10) = C(20,10)*C(25,10) = 184756*3268760 = 603923022560.
%t A113894 Table[Binomial[2n,n]Binomial[2n+5,n],{n,0,20}] (* _Harvey P. Dale_, Apr 11 2020 *)
%o A113894 (PARI) a(n) = {binomial(2*n, n) * binomial(5+2*n, n)} \\ _Andrew Howroyd_, Jan 07 2020
%o A113894 (Magma)
%o A113894 A113894:= func< n | (n+1)*Catalan(n)*Binomial(2*n+5,n) >;
%o A113894 [A113894(n): n in [0..30]]; // _G. C. Greubel_, Mar 01 2025
%o A113894 (SageMath)
%o A113894 def A113894(n): return binomial(2*n,n)*binomial(2*n+5,n)
%o A113894 print([A113894(n) for n in range(31)]) # _G. C. Greubel_, Mar 01 2025
%Y A113894 Cf. A062190.
%K A113894 easy,nonn
%O A113894 0,2
%A A113894 _Zerinvary Lajos_, Jan 28 2006
%E A113894 Name edited and terms a(13) and beyond from _Andrew Howroyd_, Jan 07 2020