A172010 a(n) = 2*A142458(2*n, n)/(n+1).

1, 26, 2741, 683870, 315704418, 234725594388, 257237392999893, 390832857108454838, 787178784737043042806, 2031210797603911366282796, 6536955866068372922068141666, 25676217636579568989377656129516, 120915166829869713032692550819662756, 672580820552232143302651758669053327784

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, A177042, A177043.

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]];
a[n_]:= 2*T[2*n,n,3]/(n+1);
Table[a[n], {n,30}] (* modified by G. C. Greubel, Mar 14 2022 *)

Sage

@CachedFunction
def T(n,k,m): # A142458
    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)
[2*T(2*n,n,3)/(n+1) for n in (1..30)] # G. C. Greubel, Mar 14 2022

Formula

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

Extensions

Name corrected and more terms added by G. C. Greubel, Mar 14 2022