A088679 a(n) = a(n-1)^2 * n / (n-1), n>1, a(0) = 0, a(1) = 1.

0, 1, 2, 6, 48, 2880, 9953280, 115579079884800, 15266884236590834264309760000, 262212473580148912869121218589990322256745385164800000000

Offset

0,3

Comments

Unreduced numerators of: f(1) = 1, f(n) = f(n-1) + f(n-1)/(n-1). - Daniel Suteu, Jul 29 2016

Links

Table of n, a(n) for n=0..9.

Andressa Paola Cordeiro, Alexandre Tavares Baraviera, and Alex Jenaro Becker, Entropy for k-trees defined by k transition matrices, arXiv:2307.05850 [math.DS], 2023. See p. 13.

Formula

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).

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

a(n)^2 = n * A052129(n). Michael Somos, May 13 2012

a(n+1)/A052129(n) = n+1. - Daniel Suteu, Jul 29 2016

Example

x + 2*x^2 + 6*x^3 + 48*x^4 + 2880*x^5 + 9953280*x^6 + ...

Mathematica

Join[{0}, RecurrenceTable[{a[1]==1, a[n]==a[n-1]^2 n/(n-1)}, a, {n, 10}]] (* Harvey P. Dale, Jan 16 2015 *)

Prog

(PARI) {a(n) = if( n<2, n>0, a(n-1)^2 * n / (n-1))}

Crossrefs

Cf. A052129.

Sequence in context: A230053 A245283 A126023 * A161766 A074020 A080310

Adjacent sequences: A088676 A088677 A088678 * A088680 A088681 A088682

Keyword

nonn

Author

Michael Somos, Oct 05 2003

Status

approved