cp's OEIS Frontend

A274269 a(n) = (5*n - 1)^(n-1).

%I A274269 #9 Sep 08 2022 08:46:17
%S A274269 1,9,196,6859,331776,20511149,1544804416,137231006679,14048223625216,
%T A274269 1628413597910449,210832519264920576,30155888444737842659,
%U A274269 4722366482869645213696,803596764671634487466709,147653612273582215982104576,29134419507545592909032289199
%N A274269 a(n) = (5*n - 1)^(n-1).
%C A274269 Compare with A052782.
%F A274269 E.g.f. A(x) = 1 - exp(-1/5*T(5*x)) = x + 9*x^2/2! + 14^2*x^3/3! + 19^3*x^4/4! + 24^4*x^5/5! + ..., where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is Euler's tree function - see A000169.
%F A274269 A(x) = series reversion( (1 - x)^5*log(1/(1 - x)) ). See A274270.
%F A274269 1 - A(x) = exp(-x/(1 - A(x))^5) = exp(-x/(exp(-5*x/(exp(-5*x/ ...))))).
%F A274269 1 - A(-x*exp(5*x)) = exp(x) = 1/(1 - A(x*exp(-5*x))).
%F A274269 1/(1 - A(x)) = Sum_{n >= 0} (5*n + 1)^(n-1)*x^n/n!, the e.g.f. for A052782.
%p A274269 A274269 := n -> (5*n - 1)^(n-1):
%p A274269 seq(A274269(n), n = 1..20);
%t A274269 Table[(5*n-1)^(n-1), {n,1,25}] (* _G. C. Greubel_, Jun 19 2016 *)
%o A274269 (Magma) [(5*n-1)^(n-1): n in [1..25]]; // _Vincenzo Librandi_, Jun 20 2016
%Y A274269 Cf. A000169, A052782, A274265, A274267, A274270.
%K A274269 nonn,easy
%O A274269 1,2
%A A274269 _Peter Bala_, Jun 19 2016