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A335849
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * Bell(k-1) * a(n-k).
0
1, 1, 3, 14, 87, 675, 6282, 68201, 846183, 11811048, 183176577, 3124958179, 58157682072, 1172551946395, 25459025908899, 592263131497942, 14696581853565723, 387477880784385143, 10816856730117090114, 318739828787430822853, 9886623306152849028771
OFFSET
0,3
FORMULA
E.g.f.: exp(1) / (exp(1) + Ei(1) - Ei(exp(x))), where Ei() is the exponential integral.
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] BellB[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
nmax = 20; CoefficientList[Series[Exp[1]/(Exp[1] + ExpIntegralEi[1] - ExpIntegralEi[Exp[x]]), {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 26 2020
STATUS
approved