A335849 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * Bell(k-1) * a(n-k).

1, 1, 3, 14, 87, 675, 6282, 68201, 846183, 11811048, 183176577, 3124958179, 58157682072, 1172551946395, 25459025908899, 592263131497942, 14696581853565723, 387477880784385143, 10816856730117090114, 318739828787430822853, 9886623306152849028771

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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

Cf. A000110, A004122, A083355, A129247, A137551.

Sequence in context: A132624 A121587 A332256 * A185323 A222714 A199548

Adjacent sequences: A335846 A335847 A335848 * A335850 A335851 A335852

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 26 2020

Status

approved