A061322 a(n) = a(n-1) * (1 + a(n-1)/n^2) with a(0) = 2.

2, 6, 15, 40, 140, 924, 24640, 12415040, 2408343949440, 71606426901226335015040, 51274803735606705472274088614112357905277056, 21728144612603201307908899563300049012978385050783094682272184269369267136230071558272

Offset: 0

Author

Henry Bottomley, Apr 24 2001

Keywords

• nonn

Comments

Only first 42 terms are integers (see A003504).

Examples

			a(2) = 6 * (1 + 6/2^2) = 15.
		

Links

• Eric Weisstein's World of Mathematics, Goebel's Sequence.

Programs

Mathematica

Block[{n = 0}, NestList[#*(1 + #/++n^2) &, 2, 11]] (* Paolo Xausa, Apr 17 2024 *)

PARI

{a(n) = local(x); if( n<1, 2 * (n==0), (x = a(n-1)) + (x/n)^2)} /* Michael Somos, Apr 02 2006 */

Formula

a(n) = a(n-1) + A003504(n+1)^2, a(n-1) = n * A003504(n+1). a(n) = A061314(2, n).