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

3, 118, 20343, 8530698, 6711481694, 8575821262764, 16243345162977759, 42826533033277249154, 150138953276380791799098, 675925071086215282939520628, 3802445616812067139270851537718, 26147695687370407271086390933321188, 215852465255521412471161891166554453788

Offset: 1

Author

Roger L. Bagula, Nov 19 2010

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..180

Crossrefs

Cf. A142458, A142459, A172010.

Programs

Mathematica

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]];
A142459[n_, k_]:= A142459[n, k]= T[n,k,4];
A172013[n_]:= A172013[n]= 6*A142459[2*n, n]/(n+1);
Table[A172013[n], {n,30}] (* modified by G. C. Greubel, Mar 18 2022 *)

Sage

@CachedFunction
def T(n,k,m):
    if (k==1 or k==n): return 1
    else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)
def A142459(n,k): return T(n,k,4)
def A172013(n): return 6*A142459(2*n, n)/(n+1)
[A172013(n) for n in (1..30)] # G. C. Greubel, Mar 18 2022

Formula

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

Extensions

Offset and formula corrected by G. C. Greubel, Mar 18 2022