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

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

C. G. Bower, Transforms (2)

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

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 *)

Prog

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

Crossrefs

Cf. A007837, A076900.

Sequence in context: A075645 A185252 A055259 * A032211 A032136 A032040

Adjacent sequences: A032296 A032297 A032298 * A032300 A032301 A032302

Keyword

nonn

Author

Christian G. Bower

Extensions

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

Status

approved