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%I #14 Mar 14 2023 08:41:24
%S 1,4,17,82,457,2936,21529,178102,1644017,16768972,187417921,
%T 2278607354,29947410937,423169937152,6398329449737,103084196690206,
%U 1763095226149729,31906336189354772,609120963614954737
%N Expansion of exp(x)*(1+x)/(1-x)^2.
%C Binomial transform of A007680.
%F E.g.f.: exp(x)(1+x)/(1-x)^2.
%F D-finite with recurrence -2*a(n) + (2*n+7)*a(n-1) - 5*n*a(n-2) + 3*(n-2)*a(n-3) = 0. - _R. J. Mathar_, Nov 09 2012
%F a(n) ~ n! * 2*exp(1)*n. - _Vaclav Kotesovec_, Jul 02 2015
%t CoefficientList[Series[E^x*(1+x)/(1-x)^2, {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jul 02 2015 *)
%Y Cf. A082029.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 01 2003
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