A088491 a(n) = floor(p(n)/p(n-1)), where p(n) = n!/(Product_{j=1..floor(n/2)} A004001(j)).

2, 3, 4, 5, 3, 7, 4, 9, 3, 11, 3, 13, 3, 15, 4, 17, 3, 19, 3, 21, 3, 23, 3, 25, 3, 27, 3, 29, 3, 31, 4, 33, 3, 35, 3, 37, 3, 39, 3, 41, 3, 43, 3, 45, 3, 47, 3, 49, 3, 51, 3, 53, 3, 55, 3, 57, 3, 59, 3, 61, 3, 63, 4, 65, 3, 67, 3, 69, 3, 71, 3, 73, 3, 75, 3, 77, 3, 79, 3, 81, 3, 83, 3, 85, 3, 87

Offset: 2

Author

Roger L. Bagula, Nov 10 2003

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..5000

Crossrefs

Cf. A004001, A088493.

Programs

Mathematica

Conway[n_]:= Conway[n]= If[n<3, 1, Conway[Conway[n-1]] +Conway[n-Conway[n-1]]];
f[n_]:= f[n]= Product[Conway[i], {i,Floor[n/2]}];
a[n_]:= a[n]= Floor[n*f[n-1]/f[n]];
Table[a[n], {n, 2, 100}] (* modified by G. C. Greubel, Mar 27 2022 *)

Sage

@CachedFunction
def b(n): # A004001
    if (n<3): return 1
    else: return b(b(n-1)) + b(n-b(n-1))
def f(n): return product( b(j) for j in (1..(n//2)) )
def A088491(n): return (n*f(n-1)//f(n))
[A088491(n) for n in (2..100)] # G. C. Greubel, Mar 27 2022

Formula

a(n) = floor(p(n)/p(n-1)), where p(n) = n!/(Product_{j=1..floor(n/2)} A004001(j)).

Extensions

Edited by G. C. Greubel, Mar 27 2022