%I #22 Jul 25 2023 10:59:21
%S 0,1,2,6,48,2880,9953280,115579079884800,
%T 15266884236590834264309760000,
%U 262212473580148912869121218589990322256745385164800000000
%N a(n) = a(n-1)^2 * n / (n-1), n>1, a(0) = 0, a(1) = 1.
%C Unreduced numerators of: f(1) = 1, f(n) = f(n-1) + f(n-1)/(n-1). - _Daniel Suteu_, Jul 29 2016
%H Andressa Paola Cordeiro, Alexandre Tavares Baraviera, and Alex Jenaro Becker, <a href="https://arxiv.org/abs/2307.05850">Entropy for k-trees defined by k transition matrices</a>, arXiv:2307.05850 [math.DS], 2023. See p. 13.
%F a(n) is asymptotic to c^(2^n)*(1-1/n+2/n^2-6/n^3+25/n^4-137/n^5+...) where c=1.28906475773... and coefficient of n^-k is (-1)^k*A084784(k).
%F a(0) = 0, a(1) = 1, a(n) = n * Product i=1..(n-1) a(i) for n > 1. - _Gerald McGarvey_, Jun 11 2004 Corrected by _Jaroslav Krizek_, Oct 16 2009
%F a(n)^2 = n * A052129(n). _Michael Somos_, May 13 2012
%F a(n+1)/A052129(n) = n+1. - _Daniel Suteu_, Jul 29 2016
%e x + 2*x^2 + 6*x^3 + 48*x^4 + 2880*x^5 + 9953280*x^6 + ...
%t Join[{0},RecurrenceTable[{a[1]==1,a[n]==a[n-1]^2 n/(n-1)},a,{n,10}]] (* _Harvey P. Dale_, Jan 16 2015 *)
%o (PARI) {a(n) = if( n<2, n>0, a(n-1)^2 * n / (n-1))}
%Y Cf. A052129.
%K nonn
%O 0,3
%A _Michael Somos_, Oct 05 2003