This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309372 #29 Aug 26 2019 04:57:11 %S A309372 0,1,12,63,208,525,1116,2107,3648,5913,9100,13431,19152,26533,35868, %T A309372 47475,61696,78897,99468,123823,152400,185661,224092,268203,318528, %U A309372 375625,440076,512487,593488,683733,783900,894691,1016832,1151073,1298188,1458975,1634256,1824877,2031708,2255643,2497600 %N A309372 a(n) = n^2 - n^3 + n^4. %H A309372 Colin Barker, <a href="/A309372/b309372.txt">Table of n, a(n) for n = 0..1000</a> %H A309372 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1). %F A309372 From _Colin Barker_, Aug 11 2019: (Start) %F A309372 G.f.: x*(1 + 3*x)*(1 + 4*x + x^2) / (1 - x)^5. %F A309372 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5. %F A309372 (End) %e A309372 a(4) = 4^2 - 4^3 + 4^4 = 16 - 64 + 256 = 208. %o A309372 (Python) %o A309372 for x in range(100): %o A309372 print((x**2)-(x**3)+(x**4)) %o A309372 (PARI) concat(0, Vec(x*(1 + 3*x)*(1 + 4*x + x^2) / (1 - x)^5 + O(x^40))) \\ _Colin Barker_, Aug 11 2019 %Y A309372 Cf. A132998. %K A309372 nonn,easy %O A309372 0,3 %A A309372 _John H. Chakkour_, Aug 02 2019