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A068102 a(n) = n! * 2^n * Sum_{i=1..n} 1/(i*2^i). 7
1, 5, 32, 262, 2644, 31848, 446592, 7150512, 128749536, 2575353600, 56661408000, 1359913708800, 35358235430400, 990036819072000, 29701191750451200, 950439443688806400, 32314962008209305600, 1163338987982963097600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

E.g.f.: -log(1-x)/(1-2*x). - Vladeta Jovovic, Feb 07 2003

a(n+1) = 2*(n+1)*a(n) + n!, a(0)=0. - Jaume Oliver Lafont, Sep 15 2009

a(n) = 2^n*n!*(log(2) - 2*(int {x=0..1} x^(2*n+1)/(1+x^2)^(n+1))dx). Thus a(n)/(2^n*n!) -> log(2) as n -> inf. Cf. A087547. - Peter Bala, Jun 21 2013

a(n) = (3*n-1)*a(n-1) - 2*(n-1)^2*a(n-2). - Vaclav Kotesovec, Aug 13 2013

The sequence b(n) = 2^n*n! = A000165(n) also satisfies the above second-order recurrence of Kotesovec. This leads to the generalized continued fraction expansion limit {n -> inf} a(n)/b(n) = log(2) = 1/(2 - 2/(5 - 8/(8 - 18/(11 - ... - 2*(n - 1)^2/((3*n - 1) - ... ))))). - Peter Bala, Feb 18 2015

MAPLE

seq(add(n!/i*2^(n-i), i=1..n), n=1..100); # Robert Israel, Aug 14 2014

MATHEMATICA

a[n_] := FullSimplify[n! (2^n Log[2] - LerchPhi[1/2, 1, 1 + n]/2)]; Array[a, 10] (* Vladimir Reshetnikov, Jan 21 2011 *)

PROG

(MAGMA) I:=[1, 5]; [n le 2 select I[n]  else (3*n-1)*Self(n-1)-2*(n-1)^2*Self(n-2): n in [1..25] ]; // Vincenzo Librandi, Feb 19 2015

CROSSREFS

Cf. A000254, A069015, A087547, A000165.

Sequence in context: A208046 A198598 A215916 * A166993 A328055 A265130

Adjacent sequences:  A068099 A068100 A068101 * A068103 A068104 A068105

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Apr 14 2002

STATUS

approved

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Last modified October 18 08:19 EDT 2021. Contains 348066 sequences. (Running on oeis4.)