cp's OEIS Frontend

A172013 a(n) = 6*A142459(2*n, n)/(n+1).

%I A172013 #16 Mar 18 2022 04:33:25
%S A172013 3,118,20343,8530698,6711481694,8575821262764,16243345162977759,
%T A172013 42826533033277249154,150138953276380791799098,
%U A172013 675925071086215282939520628,3802445616812067139270851537718,26147695687370407271086390933321188,215852465255521412471161891166554453788
%N A172013 a(n) = 6*A142459(2*n, n)/(n+1).
%H A172013 G. C. Greubel, <a href="/A172013/b172013.txt">Table of n, a(n) for n = 1..180</a>
%F A172013 a(n) = 6*A142459(2*n, n)/(n+1).
%t A172013 T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k-m+1)*T[n-1, k, m]];
%t A172013 A142459[n_, k_]:= A142459[n, k]= T[n,k,4];
%t A172013 A172013[n_]:= A172013[n]= 6*A142459[2*n, n]/(n+1);
%t A172013 Table[A172013[n], {n,30}] (* modified by _G. C. Greubel_, Mar 18 2022 *)
%o A172013 (Sage)
%o A172013 @CachedFunction
%o A172013 def T(n,k,m):
%o A172013     if (k==1 or k==n): return 1
%o A172013     else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)
%o A172013 def A142459(n,k): return T(n,k,4)
%o A172013 def A172013(n): return 6*A142459(2*n, n)/(n+1)
%o A172013 [A172013(n) for n in (1..30)] # _G. C. Greubel_, Mar 18 2022
%Y A172013 Cf. A142458, A142459, A172010.
%K A172013 nonn
%O A172013 1,1
%A A172013 _Roger L. Bagula_, Nov 19 2010
%E A172013 Offset and formula corrected by _G. C. Greubel_, Mar 18 2022