A172018 a(n) = A142458(2*n-1, n)/n.

1, 4, 182, 27410, 8890310, 5051270688, 4459786293372, 5659222645997646, 9770821427711370950, 22041005972637205198568, 62967534725721252354766676, 222256499446324679350316816644, 950020052553444052606973276792092, 4836606673194788521307702032786510240, 28920975283745982162014025622769293094712

Offset: 1

Author

Roger L. Bagula, Nov 19 2010

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..190

Crossrefs

Cf. A142458, 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]];
A172018[n_]:= T[2*n-1, n, 3]/n;
Table[A172018[n], {n, 30}] (* modified by G. C. Greubel, Mar 16 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 A172018(n): return T(2*n-1, n, 3)/n
[A172018(n) for n in (1..30)] # G. C. Greubel, Mar 16 2022

Formula

a(n) = A142458(2*n-1, n)/n.

Extensions

Offset changed and more terms added by G. C. Greubel, Mar 16 2022