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 A269428 #29 Feb 16 2025 08:33:30
%S A269428 0,-1,7,-19,41,-74,122,-186,270,-375,505,-661,847,-1064,1316,-1604,
%T A269428 1932,-2301,2715,-3175,3685,-4246,4862,-5534,6266,-7059,7917,-8841,
%U A269428 9835,-10900,12040,-13256,14552,-15929,17391,-18939,20577,-22306,24130,-26050,28070
%N A269428 Alternating sum of heptagonal pyramidal numbers.
%H A269428 OEIS Wiki, <a href="http://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H A269428 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>
%H A269428 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalPyramidalNumber.html">Heptagonal Pyramidal Number</a>
%H A269428 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-2,2,3,1).
%F A269428 G.f.: x*(1 - 4*x)/((x - 1)*(x + 1)^4).
%F A269428 a(n) = ((20*n^3 + 42*n^2 + 4*n - 9)*(-1)^n + 9)/48.
%F A269428 a(n) = Sum_{k = 0..n} (-1)^k*A002413(k).
%F A269428 Sum_{n>=1} 1/a(n) = -0.8939139178060972723185724267951741... . - _Vaclav Kotesovec_, Feb 26 2016
%F A269428 E.g.f.: (9*sinh(x) - (33*x - 51*x^2 + 10*x^3)*exp(-x))/24. - _Franck Maminirina Ramaharo_, Nov 11 2018
%t A269428 Table[((20 n^3 + 42 n^2 + 4 n - 9) (-1)^n + 9)/48, {n, 0, 40}]
%t A269428 LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 7, -19, 41}, 41]
%o A269428 (Magma) [((20*n^3+42*n^2+4*n-9)*(-1)^n+9)/48: n in [0..50]]; // _Vincenzo Librandi_, Feb 26 2016
%o A269428 (PARI) a(n)=((20*n^3 + 42*n^2 + 4*n - 9)*(-1)^n + 9)/48 \\ _Charles R Greathouse IV_, Jul 26 2016
%Y A269428 Cf. A000292, A002413, A002717, A173196, A266677.
%K A269428 sign,easy
%O A269428 0,3
%A A269428 _Ilya Gutkovskiy_, Feb 26 2016