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 A274270 #16 Feb 02 2023 05:00:55
%S A274270 1,9,47,154,274,120,-120,240,-720,2880,-14400,86400,-604800,4838400,
%T A274270 -43545600,435456000,-4790016000,57480192000,-747242496000,
%U A274270 10461394944000,-156920924160000,2510734786560000,-42682491371520000,768284844687360000,-14597412049059840000
%N A274270 Expansion of e.g.f. (1 + x)^5*log(1 + x).
%C A274270 The first six terms [1, 9, 47, 154, 274, 120] form row 5 of A105954 read as a triangular array.
%F A274270 a(n) = (-1)^n*120*(n - 6)! for n >= 6.
%F A274270 E.g.f.: A(x) = (1 + x)^5*log(1 + x).
%F A274270 Series reversion(A(x)) = exp(-1/5*T(-5*x)) - 1 = x - 9*x^2/2! + 14^2*x^3/3! - 19^3*x^4/4! + 24^4*x^5/5! - ... is the e.g.f. for a signed version of A274269, where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is Euler's tree function - see A000169.
%F A274270 Sum_{n>=1} 1/a(n) = 5098232/4462227 + 1/(120*e). - _Amiram Eldar_, Feb 02 2023
%e A274270 E.g.f.= x + 9*x^2/2 + 47*x^3/3! + 154*x^4/4! + 274*x^5/5! + 120*x^6/6! - 120*x^7/7! + ....
%t A274270 CoefficientList[Series[(1+t)^5 * Log[1+t], {t,1,20}],t]*Range[1,20]! (* _G. C. Greubel_, Jun 19 2016 *)
%o A274270 (Magma) [1,9,47,154,274] cat [(-1)^n*120*Factorial(n - 6): n in [6..25]]; // _Vincenzo Librandi_, Jun 20 2016
%Y A274270 Cf. A000169, A105954, A274265, A274266, A274267, A274268, A274269, A274270.
%K A274270 sign,easy
%O A274270 1,2
%A A274270 _Peter Bala_, Jun 19 2016