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%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
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