A230053 Recurrence a(n+2) = (n+2)*a(n+1)*a(n), with a(0) = a(1) = 1.

1, 1, 2, 6, 48, 1440, 414720, 4180377600, 13869489586176000, 521817332305350780518400000, 72373400562952038729626622187536384000000000, 415422642927888257689749131592471020852730170822782196121600000000000000

Offset: 0

Author

Emanuele Munarini, Oct 08 2017

Keywords

• nonn

Comments

Numbers of decimal digits in a(n) for 0 <= n <= 20: 1, 1, 1, 1, 2, 4, 6, 10, 17, 27, 44, 72, 117, 190, 307, 498, 806, 1305, 2112, 3417, 5530. - Robert Israel, Oct 09 2017

Links

• Robert Israel, Table of n, a(n) for n = 0..16

Crossrefs

Cf. A000045.

Programs

Maple

f:= proc(n) option remember; n*procname(n-1)*procname(n-2) end proc:
f(0):= 1: f(1):= 1:
map(f, [$0..12]); # Robert Israel, Oct 08 2017

Mathematica

RecurrenceTable[{a[n + 2] == (n + 2) a[n + 1] a[n], a[0] == a[1] == 1}, a, {n, 0, 12}] (* or *)
Table[Product[(n - k + 1)^Fibonacci[k], {k, 0, n - 1}], {n, 0, 12}]

Formula

a(n) = Product_{k=0..n-1} (n-k+1)^Fibonacci(k).

a(n) ~ c^(phi^n) / n, where c = exp(Sum_{k>=1} log(k+1) / (sqrt(5)*phi^k) ) = 2.32072822997682611701924627353608916645018... and phi = A001622 is the golden ratio. - Vaclav Kotesovec, Jul 05 2021, updated Mar 16 2025