A032299 "EFJ" (unordered, size, labeled) transform of 1,2,3,4,...

1, 1, 2, 9, 16, 85, 516, 1519, 6280, 45441, 431740, 1394371, 8370924, 43960657, 459099018, 6135631545, 23813007376, 150537761905, 1029390040764, 7519458731131, 101693768415220, 1909742186139921, 8269148260309882, 60924484457661793, 417027498430063800

Offset: 0

Author

Christian G. Bower

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• C. G. Bower, Transforms (2)

Crossrefs

Cf. A007837, A076900.

Programs

Mathematica

mmax = 25;
egf = Product[1 + x^m/(m - 1)!, {m, 1, mmax}] + O[x]^mmax;
CoefficientList[egf, x] * Range[0, mmax - 1]! (* Jean-François Alcover, Sep 23 2019 *)

PARI

seq(n)={Vec(serlaplace(prod(k=1, n, 1 + k*x^k/k! + O(x*x^n))))} \\ Andrew Howroyd, Sep 11 2018

Formula

E.g.f.: Product_{m>0} (1+x^m/(m-1)!). - Vladeta Jovovic, Nov 26 2002

E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*x^(j*k)/(k*((j - 1)!)^k)). - Ilya Gutkovskiy, Sep 13 2018

Extensions

a(0)=1 prepended and terms a(23) and beyond from Andrew Howroyd, Sep 11 2018