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 A274266 #17 Feb 02 2023 05:01:13
%S A274266 1,5,11,6,-6,12,-36,144,-720,4320,-30240,241920,-2177280,21772800,
%T A274266 -239500800,2874009600,-37362124800,523069747200,-7846046208000,
%U A274266 125536739328000,-2134124568576000,38414242234368000,-729870602452992000,14597412049059840000
%N A274266 Expansion of e.g.f. (1 + x)^3*log(1 + x).
%C A274266 First four terms [1, 5, 11, 6] form row 3 of A105954 read as a triangular array.
%F A274266 a(n) = (-1)^n*6*(n - 4)! for n >= 4.
%F A274266 E.g.f.: A(x) = (1 + x)^3*log(1 + x).
%F A274266 Series reversion(A(x)) = exp(-1/3*T(-3*x)) - 1 = x - 5*x^2/2! + 8^2*x^3/3! - 11^3*x^4/4! + 14^4*x^5/5! - ... is the e.g.f. for a signed version of A274265, where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is Euler's tree function - see A000169.
%F A274266 Sum_{n>=1} 1/a(n) = 71/55 + 1/(6*e). - _Amiram Eldar_, Feb 02 2023
%e A274266 E.g.f.= x + 5*x^2/2 + 11*x^3/3! + 6*x^4/4! - 6*x^5/5! + ....
%t A274266 CoefficientList[Series[(1+t)^3 * Log[1+t], {t, 1, 20}], t]*Range[1, 20]! (* _G. C. Greubel_, Jun 19 2016 *)
%o A274266 (Magma) [1,5,11] cat [(-1)^n*6*Factorial(n-4): n in [4..25]]; // _Vincenzo Librandi_, Jun 20 2016
%Y A274266 Cf. A000169, A105954, A274265, A274268, A274270.
%K A274266 sign,easy
%O A274266 1,2
%A A274266 _Peter Bala_, Jun 19 2016