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 A269441 #11 Feb 16 2025 08:33:30
%S A269441 0,-1,10,-28,62,-113,188,-288,420,-585,790,-1036,1330,-1673,2072,
%T A269441 -2528,3048,-3633,4290,-5020,5830,-6721,7700,-8768,9932,-11193,12558,
%U A269441 -14028,15610,-17305,19120,-21056,23120,-25313,27642,-30108,32718,-35473,38380,-41440,44660
%N A269441 Alternating sum of 10-gonal (or decagonal) pyramidal numbers.
%H A269441 OEIS Wiki, <a href="http://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H A269441 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>
%H A269441 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-2,2,3,1).
%F A269441 G.f.: x*(1 - 7*x)/((x - 1)*(x + 1)^4).
%F A269441 a(n) = ((-1)^n*(16*n^3 + 30*n^2 - 4*n - 9) + 9) /24.
%F A269441 a(n) = Sum_{k = 0..n} (-1)^k*A007585(k).
%F A269441 Sum_{n>=1} 1/a(n) = -0.9251958836055717745244669... . - _Vaclav Kotesovec_, Feb 26 2016
%t A269441 Table[((-1)^n (16 n^3 + 30 n^2 - 4 n - 9) + 9)/24, {n, 0, 40}]
%t A269441 LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 10, -28, 62}, 41]
%o A269441 (Magma) [((-1)^n*(16*n^3+30*n^2-4*n-9)+9)/24: n in [0..40]]; // _Vincenzo Librandi_, Feb 27 2016
%Y A269441 Cf. A000292, A002717, A007585, A173196, A266677, A269428, A269429.
%K A269441 easy,sign
%O A269441 0,3
%A A269441 _Ilya Gutkovskiy_, Feb 26 2016