cp's OEIS Frontend

A193079 Decimal expansion of the constant term of the reduction of sinh(2x) by x^2->x+1.

%I A193079 #11 Jan 18 2022 02:30:07
%S A193079 2,3,6,9,1,5,8,6,9,7,9,0,0,0,9,4,4,4,0,4,6,8,2,7,2,8,0,2,2,5,8,3,8,5,
%T A193079 2,5,8,6,9,8,0,1,3,7,7,5,3,7,9,1,7,7,2,0,3,0,0,5,9,1,4,2,3,8,5,4,2,3,
%U A193079 7,6,8,5,7,0,7,5,7,9,9,8,5,9,2,2,3,3,8,9,0,0,0,6,0,1,8,0,2,1,8,2
%N A193079 Decimal expansion of the constant term of the reduction of sinh(2x) by x^2->x+1.
%C A193079 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193079 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193079 Equals Sum_{k>=1} 2^(2*k+1)*Fibonacci(2*k)/(2*k+1)!.
%F A193079 Equals ((3+sqrt(5))*sinh(1-sqrt(5)) + 2*sinh(1+sqrt(5)))/(5 + sqrt(5)). (End)
%e A193079 2.3691586979000944404682728022583852586980...
%t A193079 f[x_] := Sinh[2 x]; r[n_] := Fibonacci[n];
%t A193079 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193079 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
%t A193079 RealDigits[u0, 10]
%Y A193079 Cf. A000045, A193010, A192232, A193080.
%K A193079 nonn,cons
%O A193079 1,1
%A A193079 _Clark Kimberling_, Jul 15 2011