A029767 a(n) = (n-1)!*(2^n-1) for n>=1, a(0)=0.

0, 1, 3, 14, 90, 744, 7560, 91440, 1285200, 20603520, 371226240, 7428153600, 163459296000, 3923502105600, 102017281766400, 2856571067750400, 85698439706880000, 2742370993410048000, 93240969463369728000, 3356681303055015936000, 127554011161191014400000

Offset

0,3

Comments

Labeled octupi with n nodes.

a(n) is the number of connected endofunctions on n points such that every nonrecurrent element has at most one element in its preimage and every recurrent element has at most two elements in its preimage. - Geoffrey Critzer, Dec 07 2011

References

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, pp. 12, 55, 409.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.1.5.

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 498

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 777

Formula

E.g.f.: log(1-x)-log(1-2*x).

In Maple notation, representation as an infinite sum: a(n) = sum((n+k)!/((k+1)! *2^k), k=0..infinity)/2, n=1, 2... Representation as n-th moment of a positive function on a positive half-axis: a(n)=int(x^n*1/2*exp(-x)/x*(2*exp(1/2*x)-2), x=0..infinity), n=1, 2... - Karol A. Penson, Oct 15 2002

D-finite with recurrence: a(n) +3*(-n+1)*a(n-1) +2*(n-1)*(n-2)*a(n-2) = 0. - R. J. Mathar, Jan 08 2013

a(n) = n!*Sum_{k=0..n-1} binomial(n-1,k)/(k+1). - J. M. Bergot, Jul 30 2015

a(n) = (1/zeta(n)) * Integral_{x=0..1} (log(1/x))^(n-1) / (sqrt(x) * (1-x)) dx. - Amrik Singh Nimbran, May 06 2018

Maple

with(combinat): seq(stirling1(j, 1)*stirling2(j+1, 2)*(-1)^(j+1), j=0..16); # Zerinvary Lajos, Mar 30 2007

Mathematica

a=x/(1-x); Range[0, 20]! CoefficientList[Series[Log[1/(1-a)], {x, 0, 20}], x]  (* Geoffrey Critzer, Dec 07 2011 *)
Join[{0}, Table[(n - 1)! (2^n - 1), {n, 20}]] (* Vincenzo Librandi, Apr 18 2015 *)

Prog

(Magma) [0] cat [Factorial(n-1)*(2^n-1): n in [1..20]]; // Vincenzo Librandi, Apr 18 2015
(PARI) concat([0], for(n=1, 25, print1((n-1)!*(2^n -1), ", "))) \\ G. C. Greubel, Jan 19 2017
(GAP) Concatenation([0], List([1..20], n->Factorial(n-1)*(2^n-1))); # Muniru A Asiru, Aug 09 2018

Crossrefs

Cf. A001865.

Sequence in context: A088789 A202293 A202294 * A215475 A120056 A125788

Adjacent sequences: A029764 A029765 A029766 * A029768 A029769 A029770

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved