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
KEYWORD
nonn
AUTHOR
Domingo Gomez Morin (Dgomezm(AT)etheron.net)
STATUS
approved