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