A086714 a(1) = 4, a(n) = a(n-1)*(a(n-1) - 1)/2.

4, 6, 15, 105, 5460, 14903070, 111050740260915, 6166133456248548335768188155, 19010600900133834176644234577571914951562754277857057935

Offset: 1

Author

Jon Perry, Jul 29 2003

Keywords

• nonn

Comments

The next two terms, a(10) and a(11), have 111 and 221 digits. - Harvey P. Dale, Jun 10 2011

Interpretation through plane geometry: Start with the a(n)-sided regular polygon, connect all the vertices to create a figure having a(n+1)=A000217(a(n)-1) edges. Repeat to obtain this sequence. - T. D. Noe, May 13 2016

Let y(1) = x1+x2+x3+x4, and define y(n+1) as the plethysm e2[y(n)], where e2 represents the second elementary symmetric function. Then a(n) is y(n) evaluated at x1=x2=x3=x4=1. - Per W. Alexandersson, Jun 06 2020

Each term is the number of coordinate planes in Euclidean space of the dimensionality of the previous term. - Shel Kaphan, Feb 06 2023

Examples

			a(2) = a(1)*(a(1)-1)/2 = 4*3/2 = 6.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..13

Crossrefs

Cf. A251702, A251794, A006893.

Cf. A000217, A007501, A013589, A050542, A050548, A050536, A050909.

Programs

Mathematica

RecurrenceTable[{a[1]==4,a[n]==(a[n-1](a[n-1]-1))/2},a[n],{n,10}] (* Harvey P. Dale, Jun 10 2011 *)

PARI

v=vector(10,i,(i==1)*4); for(i=2,10,v[i]=v[i-1]*(v[i-1]-1)/2); v

PARI

a086714(upto)={my(a217(n)=n*(n+1)/2,a=4);for(k=1,upto,print1(a,", ");a=a217(a-1))};
a086714(9) \\ Hugo Pfoertner, Sep 18 2021

Formula

Limit_{n->oo} a(n)^(1/2^n) = 1.280497808541657066685323460209089278782... (see A251794). - Vaclav Kotesovec, Feb 15 2014, updated Dec 09 2014

a(n) ~ 2 * A251794^(2^n). - Vaclav Kotesovec, Dec 09 2014

a(n+1) = binomial(a(n), 2). - Shel Kaphan, Feb 06 2023