%I #50 Dec 27 2022 15:02:34
%S 1,3,7,12,18,25,33,42,52,63,75,88,102,117,133,150,168,187,207,228,250,
%T 273,297,322,348,375,403,432,462,493,525,558,592,627,663,700,738,777,
%U 817,858,900,943,987,1032,1078
%N Expansion of (1+x^2-x^3)/(1-x)^3.
%H G. C. Greubel, <a href="/A027379/b027379.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n*(n+5)/2 = A000217(n+2) - 3 for n>=1. - _Emeric Deutsch_, Mar 01 2004
%F a(n) = n + a(n-1) + 2, n>1. - _Vincenzo Librandi_, Dec 06 2009
%F E.g.f.: 1 + x*(x + 6)*exp(x)/2. - _G. C. Greubel_, May 14 2017
%o (PARI) a(n)=if(n,n*(n+5)/2,1) \\ _Charles R Greathouse IV_, Jun 11 2015
%o (Magma) [n eq 0 select 1 else n*(n+5)/2: n in [0..50]]; // _G. C. Greubel_, Jul 31 2022
%o (SageMath) [n*(n+5)/2 + bool(n==0) for n in (0..50)] # _G. C. Greubel_, Jul 31 2022
%Y Essentially the triangular numbers (A000217) minus 3.
%Y Also essentially the same as A055998.
%Y Cf. A000217, A034856, A046691.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_