A376057 - OEIS

%I #21 Oct 29 2024 17:10:20

%S 1,2,14,994,6917246,430634636937890,2039908095836912108987531110990,

%T 54095925512992695768212345567905438957243461489279855615252290

%N a(n) is the denominator of the sum S(n) defined in A376056.

%H Alois P. Heinz, <a href="/A376057/b376057.txt">Table of n, a(n) for n = 0..11</a>

%F a(n+1) = (2*n+1)*a(n)^2 + a(n), with a(0) = 1.

%e The first few values of S(n) are 0/1, 1/2, 13/14, 993/994, 6917245/6917246, 430634636937889/430634636937890, ...

%p a:= proc(n) a(n):= `if`(n=0, 1, ((2*n-1)*a(n-1)+1)*a(n-1)) end:

%p seq(a(n), n=0..7);  # _Alois P. Heinz_, Oct 18 2024

%t RecurrenceTable[{a[n+1] == (2*n+1)*a[n]^2 + a[n], a[0] == 1}, a, {n, 0, 7}] (* _Amiram Eldar_, Sep 15 2024 *)

%Y Cf. A374663, A375516, A375531, A375532, A375781, A375522, A376048-A376056.

%K nonn,base,frac

%O 0,2

%A _N. J. A. Sloane_, Sep 14 2024.

%E a(0)=1 prepended by _Alois P. Heinz_, Oct 18 2024