A122648 Expansion of e.g.f.: exp(x^2)*(exp(2*x)+1)/2.

1, 1, 4, 10, 44, 156, 752, 3256, 17040, 84496, 475712, 2611104, 15687872, 93376960, 594638592, 3786534784, 25412227328, 171474649344, 1206965027840, 8569374206464, 63003419470848, 468111364627456, 3582366347030528, 27733474149611520, 220255800262627328

Offset

0,3

Links

Table of n, a(n) for n=0..24.

C.-O. Chow, Counting involutory, unimodal and alternating signed permutations, Discr. Math. 306 (2006), 2222-2228.

Formula

a(n) ~ exp(sqrt(2*n)-n/2-1/2)*2^(n/2-3/2)*n^(n/2). - Vaclav Kotesovec, Jun 27 2013

Conjecture: D-finite with recurrence a(n) -2*a(n-1) +2*(-2*n+3)*a(n-2) +4*(n-2)*a(n-3) +4*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Aug 20 2021

Mathematica

CoefficientList[Series[E^(x^2)*(E^(2*x)+1)/2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(x^2)*(exp(2*x)+1)/2))) \\ Michel Marcus, May 28 2019

Crossrefs

Sequence in context: A149223 A149224 A149225 * A058819 A052394 A197627

Adjacent sequences: A122645 A122646 A122647 * A122649 A122650 A122651

Keyword

nonn

Author

N. J. A. Sloane, Sep 22 2006

Status

approved