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 A013999 From applying the "rational mean" to the number e. 7
 1, 1, 2, 8, 42, 258, 1824, 14664, 132360, 1326120, 14606640, 175448160, 2282469840, 31972303440, 479793807360, 7679384173440, 130586660507520, 2351111258805120, 44679858911251200, 893744703503769600, 18771276190401504000, 413017883356110278400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Binomial transform of A000271. - Vladeta Jovovic, Jun 26 2007 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

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)