A082029 - OEIS

%I #15 Mar 10 2023 07:13:43

%S 1,5,26,146,904,6232,47920,409712,3873152,40220288,455828224,

%T 5604002560,74326764544,1058271540224,16104132110336,260886940141568,

%U 4483390378639360,81474025156476928,1561147449772146688

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

%C Binomial transform of A082028.

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

%F 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

%F a(n) ~ n! * 2*exp(2)*n. - _Vaclav Kotesovec_, Jul 02 2015

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

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 01 2003