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A125062 Number of increasing trees with hills of height 1. 1
1, 1, 4, 15, 68, 370, 2364, 17388, 144864, 1349136, 13894560, 156831840, 1925527680, 25550778240, 364416917760, 5559659078400, 90349397913600, 1558170228787200, 28423674336153600, 546807873520742400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

If we discard the first 1 and set a(0)=1,a(1)=4, then a(n) = (n+1)!(H(n)+1), where H(n) = Sum_{k=1..n} 1/k. - Gary Detlefs, Jul 21 2010

REFERENCES

R. P. Stanley, Enumerative Combinatorics, Vol. 1, Cambridge University Press, 1997, p25.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

E.g.f.: (1+x*log(1/(1-x)))/(1-x).

a(n) = 2*(n-1)*a(n-1) - (n^2-4*n+5)*a(n-2) - (n-3)*(n-2)*a(n-3). - Vaclav Kotesovec, Nov 19 2012

a(n) ~ n!*(log(n) + gamma + 1 + O(log(n)/n)), where gamma is Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Nov 19 2012

MATHEMATICA

With[{nn=20}, CoefficientList[Series[(1+x Log[1/(1-x)])/(1-x), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Mar 14 2012 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace((1+x*log(1/(1-x)))/(1-x))) \\ G. C. Greubel, Aug 31 2018

CROSSREFS

Sequence in context: A011967 A250886 A055732 * A039625 A020020 A000882

Adjacent sequences: A125059 A125060 A125061 * A125063 A125064 A125065

KEYWORD

nonn

AUTHOR

Wenjin Woan, Jan 09 2007

EXTENSIONS

Edited by the Associate Editors of the OEIS, Oct 05 2009

STATUS

approved

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Last modified January 26 22:13 EST 2023. Contains 359836 sequences. (Running on oeis4.)