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A087208 Expansion of e.g.f.: exp(x)/(1-x^2). 7
1, 1, 3, 7, 37, 141, 1111, 5923, 62217, 426457, 5599531, 46910271, 739138093, 7318002277, 134523132927, 1536780478171, 32285551902481, 418004290062513, 9879378882159187, 142957467201379447, 3754163975220491061 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..449

FORMULA

a(n) = Sum_{k=0..floor(n/2)} n!/(n-2*k)!.

a(n) = n*(n-1)*a(n-2) + 1. - Vladeta Jovovic, Aug 24 2004

a(n) = (A000522(n)+(-1)^n*A000166(n))/2. - Vladeta Jovovic, Aug 24 2004

a(n) = sum{k=0..n, binomial(n, k)(1+(-1)^k)k!/2} Binomial transform of A010050 (with interpolated zeros). - Paul Barry, Sep 14 2004

a(n) = Sum[P(n, k)[1, 0, 1, 0, 1, 0...](k), {k, 0, n}]. - Ross La Haye, Aug 29 2005

a(n) = (1/(2*exp(1))) * [int(t^n*exp(1-abs(1-t)), t=0..2) + int([(2+t)^n+(-t)^n] * exp(-t), t=0..infinity)]. - Groux Roland, Jan 15 2011

E.g.f.: 1/U(0) where U(k)=  1 - x^2/(1 - 1/(1 + x*(k+1)/U(k+1)) ; (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 16 2012

If n is even then a(n) ~ n!*(e/2 + 1/(2*e)) = 1.543080634815243... * n!, if n is odd then a(n) ~ n!*(e/2 - 1/(2*e)) = 1.175201193643801... * n!. - Vaclav Kotesovec, Nov 20 2012

Conjecture: a(n) -a(n-1) -n*(n-1)*a(n-2) +(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, May 29 2013

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[x]/(1-x^2), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Aug 11 2017 *)

CROSSREFS

Cf. A002747.

Sequence in context: A020463 A057625 A308392 * A161675 A208809 A086031

Adjacent sequences:  A087205 A087206 A087207 * A087209 A087210 A087211

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Oct 19 2003

EXTENSIONS

Definition clarified by Harvey P. Dale, Aug 11 2017

STATUS

approved

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Last modified July 20 23:29 EDT 2019. Contains 325189 sequences. (Running on oeis4.)