A013999 From applying the "rational mean" to the number e.

1, 1, 2, 8, 42, 258, 1824, 14664, 132360, 1326120, 14606640, 175448160, 2282469840, 31972303440, 479793807360, 7679384173440, 130586660507520, 2351111258805120, 44679858911251200, 893744703503769600, 18771276190401504000, 413017883356110278400

Offset

0,3

Comments

Binomial transform of A000271. - Vladeta Jovovic, Jun 26 2007

Conjecture: this is also the number of acyclic orientations of the complement of the path graph. - Martin Rubey, Oct 15 2023

Links

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

Domingo Gómez Morín, New Elements For The Irrational Numbers, Journal of Transfigural Mathematics, Vol. 2, No. 1, 1996.

R. P. Stanley, An Equivalence Relation on the Symmetric Group and Multiplicity-free Flag h-Vectors, preprint, 2008. - From N. J. A. Sloane, May 06 2012

Formula

G.f.: Sum_{n>=0} n!*(x*(1-x))^n. - Vladeta Jovovic, Jun 26 2007

Recurrence: a(n) = (n+3)*a(n-1) - (2*n+1)*a(n-2) + n*a(n-3). - Vaclav Kotesovec, Oct 07 2012

G.f.: 1/Q(0), where Q(k)= 1 + x/(1-x) - x*(k+2)/(1 - x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 21 2013

a(n) = sum(binomial(n-k+1,k)*(-1)^k*(n-k+1)!, k=0..floor((n+1)/2)). - Emanuele Munarini, Jul 01 2013

a(n) ~ n!*n/exp(1). - Vaclav Kotesovec, Jul 06 2013

Mathematica

Table[SeriesCoefficient[Sum[k!*(x*(1-x))^k, {k, 0, n}], {x, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 07 2012 *)

Prog

(Maxima) makelist(sum(binomial(n-k+1, k)*(-1)^k*(n-k+1)!, k, 0, floor((n+1)/2)), n, 0, 20); /* Emanuele Munarini, Jul 01 2013 */

Crossrefs

Cf. A000271.

Sequence in context: A100327 A018934 A107588 * A130649 A054993 A188912

Adjacent sequences: A013996 A013997 A013998 * A014000 A014001 A014002

Keyword

nonn

Author

Domingo Gomez Morin (Dgomezm(AT)etheron.net)

Status

approved