A172013 - OEIS

%I #16 Mar 18 2022 04:33:25

%S 3,118,20343,8530698,6711481694,8575821262764,16243345162977759,

%T 42826533033277249154,150138953276380791799098,

%U 675925071086215282939520628,3802445616812067139270851537718,26147695687370407271086390933321188,215852465255521412471161891166554453788

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

%H G. C. Greubel, <a href="/A172013/b172013.txt">Table of n, a(n) for n = 1..180</a>

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

%t 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 A142459[n_, k_]:= A142459[n, k]= T[n,k,4];

%t A172013[n_]:= A172013[n]= 6*A142459[2*n, n]/(n+1);

%t Table[A172013[n], {n,30}] (* modified by _G. C. Greubel_, Mar 18 2022 *)

%o (Sage)

%o @CachedFunction

%o def T(n,k,m):

%o     if (k==1 or k==n): return 1

%o     else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)

%o def A142459(n,k): return T(n,k,4)

%o def A172013(n): return 6*A142459(2*n, n)/(n+1)

%o [A172013(n) for n in (1..30)] # _G. C. Greubel_, Mar 18 2022

%Y Cf. A142458, A142459, A172010.

%K nonn

%O 1,1

%A _Roger L. Bagula_, Nov 19 2010

%E Offset and formula corrected by _G. C. Greubel_, Mar 18 2022