A082029 Expansion of exp(2*x)*(1+x)/(1-x)^2.

1, 5, 26, 146, 904, 6232, 47920, 409712, 3873152, 40220288, 455828224, 5604002560, 74326764544, 1058271540224, 16104132110336, 260886940141568, 4483390378639360, 81474025156476928, 1561147449772146688

Offset

0,2

Comments

Binomial transform of A082028.

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: exp(2*x)*(1+x)/(1-x)^2.

D-finite with recurrence -(2*n+3)*a(n) + (2*n^2+9*n+14)*a(n-1) - 2*(2*n+5)*(n-1)*a(n-2) = 0. - R. J. Mathar, Nov 12 2012

a(n) ~ n! * 2*exp(2)*n. - Vaclav Kotesovec, Jul 02 2015

Mathematica

CoefficientList[Series[E^(2*x)*(1+x)/(1-x)^2, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 02 2015 *)

Crossrefs

Sequence in context: A183161 A351151 A263134 * A365150 A081047 A001705

Adjacent sequences: A082026 A082027 A082028 * A082030 A082031 A082032

Keyword

easy,nonn

Author

Paul Barry, Apr 01 2003

Status

approved