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 A274268 #20 Feb 02 2023 06:24:29
%S A274268 1,7,26,50,24,-24,48,-144,576,-2880,17280,-120960,967680,-8709120,
%T A274268 87091200,-958003200,11496038400,-149448499200,2092278988800,
%U A274268 -31384184832000,502146957312000,-8536498274304000,153656968937472000,-2919482409811968000,58389648196239360000
%N A274268 Expansion of e.g.f. (1 + x)^4*log(1 + x).
%C A274268 First five terms [1, 7, 26, 50, 24] form row 4 of A105954 read as a triangular array.
%F A274268 a(n) = (-1)^(n-1)*24*(n - 5)! for n >= 5.
%F A274268 E.g.f.: A(x) = (1 + x)^4*log(1 + x).
%F A274268 Series reversion(A(x)) = exp(-1/4*T(-4*x)) - 1 = x - 7*x^2/2! + 11^2*x^3/3! - 15^3*x^4/4! + 19^4*x^5/5! - ... is the e.g.f. for a signed version of A274267, where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is Euler's tree function - see A000169.
%F A274268 Sum_{n>=1} 1/a(n) = 2733/2275 + 1/(24*e). - _Amiram Eldar_, Feb 02 2023
%e A274268 E.g.f.= x + 7*x^2/2 + 26*x^3/3! + 50*x^4/4! + 24*x^5/5! - 24*x^6/6! + ...
%t A274268 CoefficientList[Series[(1+t)^4 * Log[1+t], {t, 1, 20}], t]*Range[1, 20]! (* _G. C. Greubel_, Jun 19 2016 *)
%o A274268 (Magma) [1,7,26,50] cat [(-1)^(n-1)*24*Factorial(n-5): n in [5..25]]; // _Vincenzo Librandi_, Jun 20 2016
%Y A274268 Cf. A000169, A105954, A274265, A274266, A274267, A274269, A274270.
%K A274268 sign,easy
%O A274268 1,2
%A A274268 _Peter Bala_, Jun 19 2016