A099935 - OEIS

%I #28 Feb 07 2022 08:48:39

%S 7,4,1,0,2,7,9,2,1,5,2,3,5,7,7,3,5,5,8,4,1,7,8,3,9,8,6,6,7,1,0,2,4,4,

%T 1,1,7,3,2,5,5,8,8,4,2,5,0,1,5,0,0,2,1,8,4,2,5,8,0,2,8,0,8,4,7,7,8,3,

%U 8,7,4,4,4,8,9,0,8,1,5,9,6,7,2,5,1,1,6,6,2,2,1,6,0,9,5,9,4,4,1,1,5,6,4,0

%N Decimal expansion of Sum_{k>=0} (-1)^(k+1)*A000045(k)/k!.

%C This number is the coefficient of x in the reduction of e^(-x) by the substitution x^2->x+1; see A193026 and A193010.

%F Equals exp(-1/2)*(2/sqrt(5))*sinh(sqrt(5)/2).

%F Equals A098689 / e. - _Amiram Eldar_, Feb 07 2022

%e 0.74102792152357735584178398667102441173255884250150...

%t (E^(1+2/GoldenRatio)-1) / (E^GoldenRatio*(2*GoldenRatio-1)) // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Feb 13 2013 *)

%o (PARI) exp(-1/2)*(2/sqrt(5))*sinh(sqrt(5)/2) \\ _Michel Marcus_, Feb 07 2022

%Y Cf. A000045, A001113, A098689, A193010, A193026.

%K cons,nonn

%O 0,1

%A _Benoit Cloitre_, Nov 12 2004