A154596 a(n) = Sum_{j=1..n-1} A142458(n-1, k)*a(n - k), with a(1) = 1.

1, 1, 2, 11, 129, 3214, 162491, 16306117, 3231430542, 1254563121783, 953359099059949, 1417753660258148022, 4128222097278496550683, 23571703478682225135264061, 264268834213603744830353397238

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Jan 12 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..80

Crossrefs

Cf. A000670, A142458.

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]];
A142458[n_, k_]:= A142458[n, k] = T[n, k, 3];
a[n_]:= a[n]= If[n==1, 1, Sum[A142458[n-1, j]*a[n-j], {j,n-1}]];
Table[a[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 A142458(n,k): return T(n,k,3)
@CachedFunction
def A154596(n): return 1 if (n==1) else sum( A142458(n-1, j)*A154596(n-j) for j in (1..n-1) )
[A154596(n) for n in (1..30)] # G. C. Greubel, Mar 16 2022

Formula

a(n) = Sum_{j=1..n-1} A142458(n-1, k)*a(n-k), with a(1) = 1.

Extensions

Offset changed by G. C. Greubel, Mar 16 2022