A168490 Sequence with Hankel transform equal to 2^floor(n^2/2).

1, 1, 2, 6, 24, 112, 560, 2888, 15136, 80160, 427968, 2300736, 12445440, 67702272, 370205184, 2033976960, 11224014336, 62186741248, 345825348608, 1929744008192, 10802203119616, 60644473282560, 341383505977344

Offset

0,3

Comments

Hankel transform is A099202 (a trivial Somos-4 sequence linked to y^2=1-12x+44x^2-48x^3.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

G.f.: 1/(1-x/(1-x/(1-2x/(1-2x/(1-x/(1-x/(1-2x/(1-2x/(1-x/(1-x/(1-2x/(1-.... (continued fraction);

G.f.: 1/(1-x-x^2/(1-3x-4x^2/(1-3x-x^2/(1-3x-4x^2/(1-3x-x^2/(1-3x-4x^2/(1-... (continued fraction);

G.f.: (1-2x-sqrt((1-2x)(1-10x+24x^2)))/(4x(1-2x)).

Recurrence: (n+1)*a(n) = 4*(3*n-1)*a(n-1) - 4*(11*n-17)*a(n-2) + 24*(2*n-5)*a(n-3). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 2^(n-5/2)*3^(n+1)/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012

a(n) = Sum_{k, 0<=k<=n} A168511(n,k)*2^(n-k). - Philippe Deléham, Mar 19 2013

Mathematica

CoefficientList[Series[(1-2*x-Sqrt[(1-2*x)(1-10*x+24*x^2)])/(4x*(1-2*x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)

Crossrefs

Sequence in context: A177521 A152322 A308726 * A118376 A212884 A375923

Adjacent sequences: A168487 A168488 A168489 * A168491 A168492 A168493

Keyword

easy,nonn

Author

Paul Barry, Nov 27 2009

Status

approved