A070779 -id:A070779 - cp's OEIS frontend

A087860 Expansion of e.g.f.: (1-exp(x/(x-1)))/(1-x).

0, 1, 3, 10, 39, 176, 905, 5244, 34111, 250480, 2108529, 20751380, 241315151, 3282366504, 50786289385, 865850559196, 15856276032255, 306665879765984, 6199863566817761, 130237717066988580, 2832527601333186319

Offset: 0

Vladeta Jovovic, Oct 25 2003

nonn

G. C. Greubel, Table of n, a(n) for n = 0..448

Cf. A009940, A070779.

I:=[1,3,10]; [0] cat [n le 3 select I[n] else 3*(n-1)*Self(n-1) - (n-1)*(3*n-5)*Self(n-2) +(n-1)*(n-2)^2*Self(n-3): n in [1..30]];

With[{nn=20},CoefficientList[Series[(1-Exp[x/(x-1)])/(1-x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Nov 27 2015 *)

x='x+O('x^30); concat([0], Vec(serlaplace((1-exp(x/(x-1)))/(1-x)))) \\ G. C. Greubel, Feb 06 2018

a(n) = n!*(1 - LaguerreL(n, 1)).
a(n) = 3*(n-1)*a(n-1) - (n-1)*(3*n - 5)*a(n-2) + (n-2)^2*(n-1)*a(n-3). - Vaclav Kotesovec, Nov 13 2017
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) * (1 - BesselJ(0,2*sqrt(x))). - Ilya Gutkovskiy, Jul 17 2020
a(n) = n*n!*hypergeom([1 - n, 1], [2, 2], 1). - Peter Luschny, May 10 2021
a(n) ~ n! * (1 - exp(1/2)*cos(2*sqrt(n) - Pi/4) / (sqrt(Pi) * n^(1/4))). - Vaclav Kotesovec, May 10 2021

Definition clarified by Harvey P. Dale, Nov 27 2015

A274294 a(n) = 1+(n+1)^2+n!+Sum_{k=1..n-1} binomial(n,k)*n!/(n-k)!.

Original entry on oeis.org

3, 6, 16, 50, 234, 1582, 13376, 130986, 1441810, 17572214, 234662352, 3405357826, 53334454586, 896324308830, 16083557845504, 306827170866362, 6199668952527906, 132240988644216166, 2968971263911289360, 69974827707903049554, 1727194482044146637962

Offset: 0

N. J. A. Sloane, Jun 18 2016

nonn

Number of residuated maps on the lattice M_n.

Erika D. Foreman, Order automorphisms on the lattice of residuated maps of some special nondistributive lattices, (2015). Univ. Louisville, Electronic Theses and Dissertations. Paper 2257.

Cf. A317094.

f:=n->1+(n+1)^2+n!+add(binomial(n,k)*n!/(n-k)!,k=1..n-1);
[seq(f(n),n=0..20)];

Table[1+(n+1)^2+n!+Sum[Binomial[n,k] n!/(n-k)!,{k,n-1}],{n,0,20}] (* Harvey P. Dale, Feb 17 2023 *)

a(n) = (n+1)^2 +n! + A070779(n-1), n>=1. - R. J. Mathar, Jul 16 2020

cp's OEIS Frontend

A087860 Expansion of e.g.f.: (1-exp(x/(x-1)))/(1-x).

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