A145386 a(1) = 1; a(n) = a(n-1)*(2*(n-1)+a(n-1)) for n > 1.

1, 3, 21, 567, 326025, 106295560875, 11298746263006377496125, 127661667115800580590177504581888913674961375

Offset

1,2

Comments

Next term has 89 decimal digits and is too large to include. - Klaus Brockhaus, Oct 13 2008

Links

Table of n, a(n) for n=1..8.

Formula

a(n) = Product_{k = 1..n} b(k), where b(1) = 1 and b(n) = a(n-1) + 2*(n-1) for n > 1. The sequence b(n) begins [1, 3, 7, 27, 575, 326035, ...] and is given by the recurrence b(n) = b(n-1)^2 - 2*(n-2)*b(n-1) + 2*(n-1) with b(1) = 1. - Peter Bala, Mar 27 2018

Example

a(2) = a(1)*(2*(2-1)+a(1)) = 1*(2*1+1) = 3. - Klaus Brockhaus, Oct 13 2008

Mathematica

lst={}; s=1; Do[s*=(n+=s+n); AppendTo[lst, s], {n, 0, 7}]; lst

Prog

(ARIBAS) a:=1; for n:=1 to 9 do a:=a*(a+2*(n-1)); write(a:group(0), ", "); end; end; (* Klaus Brockhaus, Oct 13 2008 *)
(PARI) a=vector(15); a[1]=1; for(n=2, #a, a[n] = a[n-1]*(2*(n-1)+a[n-1])); a \\ Altug Alkan, Mar 27 2018

Crossrefs

Sequence in context: A006927 A014375 A135748 * A344260 A135327 A128679

Adjacent sequences: A145383 A145384 A145385 * A145387 A145388 A145389

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Oct 10 20

Extensions

Name edited by Klaus Brockhaus, Oct 13 2008

Status

approved