A343263 a(0) = 1; a(n+1) = exp(-a(n)) * Sum_{k>=0} a(n)^k * k^n / k!.
1, 1, 1, 2, 22, 301554, 2493675105669492542968967478
Offset: 0
Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 1, k] a[n - 1]^k, {k, 0, n - 1}]; Table[a[n], {n, 0, 6}] a[0] = 1; a[n_] := a[n] = BellB[n - 1, a[n - 1]]; Table[a[n], {n, 0, 6}]
Formula
a(0) = 1; a(n+1) = n! * [x^n] exp(a(n) * (exp(x) - 1)).
a(0) = 1; a(n+1) = Sum_{k=0..n} Stirling2(n,k) * a(n)^k.
Comments