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 A377398 #20 Oct 27 2024 23:44:30
%S A377398 1,-3,3,9,3,-63,-357,-1431,-5037,-16623,-52917,-164871,-506877,
%T A377398 -1545183,-4684677,-14152311,-42653517,-128353743,-385847637,
%U A377398 -1159115751,-3480492957,-10447770303,-31355893797,-94092847191,-282328873197,-847087282863,-2541463175157
%N A377398 Expansion of e.g.f. (2 - exp(x))^3.
%H A377398 Seiichi Manyama, <a href="/A377398/b377398.txt">Table of n, a(n) for n = 0..1000</a>
%H A377398 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F A377398 a(n) = 5*a(n-1) - 6*a(n-2) - 24 for n > 2.
%F A377398 a(n) = Sum_{k=0..3} (-1)^k * k! * binomial(3,k) * Stirling2(n,k).
%F A377398 a(n) = Sum_{k=0..3} (-1)^k * 2^(3-k) * binomial(3,k) * k^n.
%F A377398 G.f.: (1-4*x) * (1-5*x+12*x^2)/((1-x) * (1-2*x) * (1-3*x)).
%F A377398 a(n) = 3*2^(n+1) - 3^n - 12 for n > 0. - _Stefano Spezia_, Oct 27 2024
%F A377398 a(0) = 1; a(n) = Sum_{k=1..n} (1 - 4 * k/n) * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Oct 27 2024
%o A377398 (PARI) a(n) = sum(k=0, 3, (-1)^k*k!*binomial(3, k)*stirling(n, k, 2));
%o A377398 (PARI) a(n) = sum(k=0, 3, (-1)^k*2^(3-k)*binomial(3, k)*k^n);
%Y A377398 Cf. A226515, A377399.
%K A377398 sign,easy
%O A377398 0,2
%A A377398 _Seiichi Manyama_, Oct 27 2024