A007704 a(n+2) = (a(n) - 1)*a(n+1) + 1.

2, 3, 4, 9, 28, 225, 6076, 1361025, 8268226876, 11253255215681025, 93044467205527772332546876, 1047053135870867396062743192203958743681025

Offset: 1

Author

N. J. A. Sloane, Jeffrey Shallit

Keywords

• nonn
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..18
• J. L. Davison and Jeffrey O. Shallit, Continued Fractions for Some Alternating Series, Monatshefte für Mathematik, Vol. 111 (1991), pp. 119-126; alternative link.

Crossrefs

Cf. A006277.

Programs

Maple

A007704 := proc(n) options remember; if n <= 2 then RETURN(n+1) else (A007704(n-2)-1)*A007704(n-1)+1; fi; end;

Mathematica

RecurrenceTable[{a[n] == a[n-1] (a[n-2] - 1) + 1, a[1] == 2, a[2] == 3}, a, {n, 1, 12}] (* Jean-François Alcover, Apr 05 2020 *)

Formula

a(n) = A006277(n) + 1. - R. J. Mathar, Apr 27 2007

Product_{k=1..n} a(k) = A006277(k)*A006277(k+1). - Amiram Eldar, Mar 19 2024