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 A001863 Normalized total height of rooted trees with n nodes. (Formerly M3614 N1466) 9
 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. FORMULA E.g.f.: -exp(1)*x*(Ei(-1-LambertW(-x))-Ei(-1)) -LambertW(-x) +log(1+LambertW(-x)). - Vladeta Jovovic, Sep 29 2003 a(n)*(n-1) = A000435(n). - M. F. Hasler, Dec 10 2018 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-François 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) apply( A001863(n)=sum(k=0, n-2, (n-2)!/k!*n^k), [1..20]) \\ This defines the function A001863; apply(...) provides a check and illustration. - G. C. Greubel, Nov 14 2017, edited by M. F. Hasler, Dec 09 2018 (MAGMA) [0] cat [&+[Factorial(n-2)*n^k div Factorial(k): k in [0..n-2]]: n in [2..24]]; // Vincenzo Librandi, Dec 10 2018 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 STATUS approved

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Last modified May 27 18:56 EDT 2020. Contains 334664 sequences. (Running on oeis4.)