A179540 a(0)=0, a(1)=1, a(n)=2*n*(a(n-1)+a(n-2)), n>1.

0, 1, 4, 30, 272, 3020, 39504, 595336, 10157440, 193549968, 4074148160, 93889358816, 2351124167424, 63570351682240, 1845801323790592, 57281150264184960, 1892062450815217664, 66277682436699689216, 2454110815950536647680, 95774762938714980802048

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..400

Célia Biane, Greg Hampikian, Sergey Kirgizov, and Khaydar Nurligareev, Endhered patterns in matchings and RNA, arXiv:2404.18802 [math.CO], 2024. See pp. 8-9.

Formula

G.f.: (1/G(0)-1)/x/2 where G(k)= 1 - 4*x*k - x^2*(2*k+1)*(2*k+2)/G(k+1); (continued fraction, 1-step). - Sergei N. Gladkovskii, Jul 10 2012

a(n) ~ sqrt(2)*2^n*n^(n+1)/exp(n+1/2). - Vaclav Kotesovec, Aug 15 2013

E.g.f.: x*exp(-x)/(1-2*x)^(3/2). - Vaclav Kotesovec, Feb 23 2014

Example

a(2)=4*(0+1)=4, a(3)=6*(4+1)=30, a(4)=8*(30+4)=272...

Mathematica

RecurrenceTable[{a[0]==0, a[1]==1, a[n]==2n(a[n-1]+a[n-2])}, a[n], {n, 30}] (* Harvey P. Dale, Jun 01 2012 *)
CoefficientList[Series[x*E^(-x)/(1-2*x)^(3/2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 23 2014 *)

Crossrefs

Sequence in context: A215698 A367872 A376326 * A370346 A375172 A274665

Adjacent sequences: A179537 A179538 A179539 * A179541 A179542 A179543

Keyword

nonn

Author

Gary Detlefs, Jul 18 2010

Extensions

Corrected and extended by Harvey P. Dale, Jun 01 2012

Status

approved