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

%I A154596 #8 Mar 17 2022 01:16:18
%S A154596 1,1,2,11,129,3214,162491,16306117,3231430542,1254563121783,
%T A154596 953359099059949,1417753660258148022,4128222097278496550683,
%U A154596 23571703478682225135264061,264268834213603744830353397238
%N A154596 a(n) = Sum_{j=1..n-1} A142458(n-1, k)*a(n - k), with a(1) = 1.
%H A154596 G. C. Greubel, <a href="/A154596/b154596.txt">Table of n, a(n) for n = 1..80</a>
%F A154596 a(n) = Sum_{j=1..n-1} A142458(n-1, k)*a(n-k), with a(1) = 1.
%t A154596 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 A154596 A142458[n_, k_]:= A142458[n, k] = T[n, k, 3];
%t A154596 a[n_]:= a[n]= If[n==1, 1, Sum[A142458[n-1, j]*a[n-j], {j,n-1}]];
%t A154596 Table[a[n], {n, 30}] (* modified by _G. C. Greubel_, Mar 16 2022 *)
%o A154596 (Sage)
%o A154596 @CachedFunction
%o A154596 def T(n,k,m):
%o A154596     if (k==1 or k==n): return 1
%o A154596     else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)
%o A154596 def A142458(n,k): return T(n,k,3)
%o A154596 @CachedFunction
%o A154596 def A154596(n): return 1 if (n==1) else sum( A142458(n-1, j)*A154596(n-j) for j in (1..n-1) )
%o A154596 [A154596(n) for n in (1..30)] # _G. C. Greubel_, Mar 16 2022
%Y A154596 Cf. A000670, A142458.
%K A154596 nonn
%O A154596 1,3
%A A154596 _Roger L. Bagula_ and _Gary W. Adamson_, Jan 12 2009
%E A154596 Offset changed by _G. C. Greubel_, Mar 16 2022