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