cp's OEIS Frontend

A193027 Decimal expansion of the constant term of the reduction of e^(2x) by x^2->x+1.

%I A193027 #13 Feb 08 2025 03:42:18
%S A193027 7,2,3,9,8,7,7,3,3,1,3,0,0,9,0,0,1,7,7,3,2,4,9,3,2,2,2,3,3,9,6,1,6,1,
%T A193027 0,4,2,5,9,0,1,3,3,4,6,9,1,6,7,8,8,1,3,4,6,1,0,3,0,8,8,0,9,0,1,1,9,1,
%U A193027 0,1,2,1,1,5,7,9,3,8,8,4,9,2,0,5,8,7,9,3,1,7,7,2,9,8,3,9,6,4,3,2,8,6
%N A193027 Decimal expansion of the constant term of the reduction of e^(2x) by x^2->x+1.
%C A193027 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193027 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193027 Equals 1 + Sum_{k>=1} 2^k*Fibonacci(k-1)/k!.
%F A193027 Equals e * (cosh(sqrt(5)) - sinh(sqrt(5))/sqrt(5)). (End)
%e A193027 7.239877331300900177324932223396161042590133469167...
%t A193027 f[x_] := Exp[2 x]; r[n_] := Fibonacci[n];
%t A193027 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193027 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
%t A193027 RealDigits[u0, 10]
%Y A193027 Cf. A000045, A193010, A192232, A193028.
%K A193027 nonn,cons
%O A193027 1,1
%A A193027 _Clark Kimberling_, Jul 14 2011
%E A193027 a(100)-a(102) from _Georg Fischer_, Feb 08 2025