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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

Domingo Gómez Morín, New Elements For The Irrational Numbers, preprint 1996.

R. P. Stanley, An Equivalence Relation on the Symmetric Group and Multiplicity-free Flag h-Vectors, http://www-math.mit.edu/~rstan/papers/multfree.pdf. - From N. J. A. Sloane, May 06 2012

LINKS

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

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

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 December 6 09:25 EST 2019. Contains 329791 sequences. (Running on oeis4.)