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A001863 Normalized total height of rooted trees with n nodes.
(Formerly M3614 N1466)
7
0, 1, 4, 26, 236, 2760, 39572, 672592, 13227804, 295579520, 7398318500, 205075286784, 6236796259916, 206489747516416, 7393749269685300, 284714599444490240, 11733037015160276348, 515240326393584058368, 24019843795708471562564, 1184776250223810469888000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..385 (terms 1..100 from T. D. Noe)

H. Bergeron, E. M. F. Curado, J. P. Gazeau and L. M. C. S. Rodrigues, A note about combinatorial sequences and Incomplete Gamma function, arXiv preprint arXiv: 1309.6910 [math.CO], 2013.

J. Riordan, Letter to N. J. A. Sloane, Aug. 1970

J. Riordan and N. J. A. Sloane, Enumeration of rooted trees by total height, J. Austral. Math. Soc., vol. 10 pp. 278-282, 1969.

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

FORMULA

E.g.f.: -exp(1)*x*(Ei(-1-LambertW(-x))-Ei(-1)) -LambertW(-x) +log(1+LambertW(-x)). - Vladeta Jovovic, Sep 29 2003

MAPLE

A001863 := n->add((n-2)!*n^k/k!, k=0..n-2); #for n>1. Equals A001864/(n^2-n)

seq(simplify(GAMMA(n-1, n)*exp(n)), n=2..20); # Vladeta Jovovic, Jul 21 2005

MATHEMATICA

a[n_] := Sum[(n-2)!*n^k/k!, {k, 0, n-2}]; Table[a[n], {n, 1, 15}] (* Jean-Fran├žois Alcover, Oct 09 2012, from Maple *)

Table[Sum[(n-2)! n^k/k!, {k, 0, n-2}], {n, 30}] (* Harvey P. Dale, Jun 19 2016 *)

PROG

(PARI) for(n=1, 10, print1(sum(k=0, n-2, (n-2)! * n^k/k!), ", ")) \\ G. C. Greubel, Nov 14 2017

CROSSREFS

Cf. A000435, A001864.

Sequence in context: A124824 A000311 A244451 * A300698 A244524 A209923

Adjacent sequences:  A001860 A001861 A001862 * A001864 A001865 A001866

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 21 01:47 EDT 2018. Contains 316405 sequences. (Running on oeis4.)