%I #15 Mar 09 2021 10:01:19
%S 1,10,31,76,145,254,399,600,849,1170,1551,2020,2561,3206,3935,4784,
%T 5729,6810,7999,9340,10801,12430,14191,16136,18225,20514,22959,25620,
%U 28449,31510,34751,38240,41921,45866,50015,54444,59089,64030,69199,74680,80401,86450,92751,99396,106305,113574
%N Expansion of the o.g.f. (1 + 8*x + 10*x^2 + 8*x^3 + x^4)/((1 - x)^4*(1 + x)^2).
%C Antidiagonal sums of square array A342354.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F a(n) = (n + 1)/4*(5 - (-1)^n) - 7*binomial(n + 2, 2) + 7*binomial(n + 3, 3).
%F a(n) = (n + 1)*(14*(n + 1)^2 - 3*(-1)^n + 1)/12. - _Bruno Berselli_, Mar 09 2021
%o (Julia) [div((n + 1)*(14*(n + 1)^2 - 3*(-1)^n + 1),12) for n in 0:50] |> println # _Bruno Berselli_, Mar 09 2021
%Y Cf. A342354.
%K nonn,easy
%O 0,2
%A _Petros Hadjicostas_, Mar 09 2021