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A154596
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a(n) = Sum_{j=1..n-1} A142458(n-1, k)*a(n - k), with a(1) = 1.
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1
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1, 1, 2, 11, 129, 3214, 162491, 16306117, 3231430542, 1254563121783, 953359099059949, 1417753660258148022, 4128222097278496550683, 23571703478682225135264061, 264268834213603744830353397238
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = Sum_{j=1..n-1} A142458(n-1, k)*a(n-k), with a(1) = 1.
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MATHEMATICA
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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_]:= 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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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