cp's OEIS Frontend

A274267 a(n) = (4*n - 1)^(n-1).

%I A274267 #13 Sep 08 2022 08:46:17
%S A274267 1,7,121,3375,130321,6436343,387420489,27512614111,2251875390625,
%T A274267 208728361158759,21611482313284249,2472159215084012303,
%U A274267 309629344375621415601,42141982597572021484375,6193386212891813387462761,977480813971145474830595007,164890958756244164895763202881
%N A274267 a(n) = (4*n - 1)^(n-1).
%C A274267 Compare with A052774.
%H A274267 G. C. Greubel, <a href="/A274267/b274267.txt">Table of n, a(n) for n = 1..321</a>
%F A274267 E.g.f. A(x) = 1 - exp(-1/4*T(4*x)) = x + 7*x^2/2! + 11^2*x^3/3! + 15^3*x^4/4! + 19^4*x^5/5! + ..., where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is Euler's tree function - see A000169.
%F A274267 A(x) = series reversion( (1 - x)^4*log(1/(1 - x)) ). See A274268.
%F A274267 1 - A(x) = exp(-x/(1 - A(x))^4) = exp(-x/(exp(-4*x/(exp(-4*x/ ...))))).
%F A274267 1 - A(-x*exp(4*x)) = exp(x) = 1/(1 - A(x*exp(-4*x))).
%F A274267 1/(1 - A(x)) = Sum_{n >= 0} (4*n + 1)^(n-1)*x^n/n!, the e.g.f. for A052774.
%p A274267 A274267 := n -> (4*n - 1)^(n-1):
%p A274267 seq(A274267(n), n = 1..20);
%t A274267 Table[(4*n-1)^(n-1), {n,1,25}] (* _G. C. Greubel_, Jun 19 2016 *)
%o A274267 (Magma) [(4*n-1)^(n-1): n in [1..25]]; // _Vincenzo Librandi_, Jun 20 2016
%o A274267 (PARI) for(n=1,30, print1((4*n-1)^(n-1), ", ")) \\ _G. C. Greubel_, Nov 16 2017
%Y A274267 Cf. A000169, A052774, A274265, A274266, A274268, A274269.
%K A274267 nonn,easy
%O A274267 1,2
%A A274267 _Peter Bala_, Jun 19 2016