A286286 a(0) = 0; thereafter, a(n) = (2*n-1)*a(n-1) + 1.

0, 1, 4, 21, 148, 1333, 14664, 190633, 2859496, 48611433, 923617228, 19395961789, 446107121148, 11152678028701, 301122306774928, 8732546896472913, 270708953790660304, 8933395475091790033, 312668841628212651156, 11568747140243868092773

Offset: 0

Author

N. J. A. Sloane, May 15 2017

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..404

Crossrefs

Conjectured to give indices of records in A132424.

Cf. A001147, A002627 (similar sequence), A000522, A060196.

Programs

Mathematica

NestList[{(2 #2 - 1) #1 + 1, #2 + 1} & @@ # &, {0, 1}, 19][[All, 1]] (* Michael De Vlieger, Dec 10 2021 *)

Formula

a(n) = (2*n-1)!! * Sum_{k=1..n} 1/(2*k-1)!!. - Seiichi Manyama, Sep 02 2017

a(n) = floor((2*n-1)!!*A060196), for n > 0. - Peter McNair, Dec 10 2021

From Peter Bala, Feb 09 2024: (Start)

a(n) = 2*n*a(n-1) - (2*n - 3)*a(n-2) with a(0) = 0 and a(1) = 1.

The double factorial numbers (2*n-1)!! = A001147(n) satisfy the same recurrence, leading to the generalized continued fraction expansion Limit_{n -> oo} a(n)/(2*n-1)!! = Sum_{k >= 1} 1/(2*k-1)!! = A060196 = 1/(1 - 1/(4 - 3/(6 - 5/(8 - 7/(10 - 9/(12 - ... )))))). (End)