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 A380502 #25 Feb 09 2025 18:09:52
%S A380502 1,1,34,370,2179,8791,27586,72514,167245,348949,672706,1216546,
%T A380502 2087119,3425995,5416594,8291746,12341881,17923849,25470370,35500114,
%U A380502 48628411,65578591,87193954,114450370,148469509,190532701,242095426,304802434,380503495,471269779,579410866
%N A380502 a(n) = (7*n^6 - 21*n^5 + 55*n^4 - 75*n^3 + 70*n^2 - 36*n + 8)/8.
%C A380502 From a(1) onwards, first differences of A075664 (sum of next n cubes).
%H A380502 Kelvin Voskuijl, <a href="/A380502/b380502.txt">Table of n, a(n) for n = 0..10000</a>
%H A380502 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A380502 G.f.: (1 - 6*x + 48*x^2 + 118*x^3 + 303*x^4 + 132*x^5 + 34*x^6)/(1 - x)^7. - _Stefano Spezia_, Jan 28 2025
%t A380502 Table[(7 * n^6 - 21 * n^5 + 55 * n^4 - 75 * n^3 + 70 * n^2 - 36 * n + 8) / 8, {n, 1, 30}]
%o A380502 (PARI) a(n) = (7*n^6 - 21*n^5 + 55*n^4 - 75*n^3 + 70*n^2 - 36*n + 8)/8
%o A380502 (Python)
%o A380502 def A380502(n): return (n*(n*(n*(n*(n*(7*(n-3))+55)-75)+70)-36)>>3)+1 # _Chai Wah Wu_, Feb 09 2025
%Y A380502 Cf. A075664.
%Y A380502 Cf. A005448 (first differences of sum of next n natural numbers), A380353 (for sum of next n squares).
%K A380502 nonn,easy
%O A380502 0,3
%A A380502 _Kelvin Voskuijl_, Jan 25 2025