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A113060
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a(n)=n!*sum(bell(k+1)/k!,k=0..n), n=0,1..., where bell(n) are the Bell numbers, cf. A000110.
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1, 3, 11, 48, 244, 1423, 9415, 70045, 581507, 5349538, 54173950, 600127047, 7229169001, 94170096335, 1319764307235, 19806944750672, 316993980880556, 5389579751775611, 97018268274166055
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| Representation as an infinite sum involving generalized Laguerre polynomials, in Maple notation: a(n)=(-1)^n*n!*sum(LaguerreL(n, -n-1, p)/(p-1)!, p=1..infinity)/exp(1), n=0, 1... e.g.f.: exp(exp(x)-1+x)/(1-x).
Representation as the n-th moment of a positive weight function on a positive half-axis: The weight function is a piecewise continuous function which is a weighted infinite sum of shifted exponential distributions, in Maple notation: a(n)=int(x^n*sum(exp(p-x)*Heaviside(x-p)/(p-1)!, p=1..infinity))/(exp(1)), n=0, 1...
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CROSSREFS
| Cf. A113059.
Sequence in context: A192399 A186185 A127087 * A186374 A187249 A105151
Adjacent sequences: A113057 A113058 A113059 * A113061 A113062 A113063
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KEYWORD
| nonn
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 13 2005
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