A132959 Total number of all distinct list sizes in all partitions of [n] into lists, cf. A000262.
1, 3, 19, 109, 881, 7621, 77785, 854225, 10750465, 143737381, 2121714761, 33426065905, 568250246305, 10242445089605, 197388381934801, 4003553262384961, 86010508861504385, 1939950117886565125
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..440
Programs
-
Mathematica
Rest[ Range[0, 20]! CoefficientList[ Series[ Exp[x/(1 - x)] Sum[(-x)^k/(k!*(x^k - 1)), {k, 25}], {x, 0, 20}], x]] (* Robert G. Wilson v, Sep 13 2007 *)
Formula
E.g.f.: exp(x/(1-x))*Sum_{k>0}(1-exp(-x^k)).
Extensions
More terms from Robert G. Wilson v, Sep 13 2007