%I #7 Aug 02 2024 12:55:51
%S 2,5,3,4,3,4,2,1,0,7,8,7,3,3,2,4,0,7,4,5,6,2,5,2,5,5,8,6,2,7,1,9,3,2,
%T 0,6,4,0,3,4,3,4,1,5,2,8,1,8,4,0,7,5,6,5,7,7,1,3,0,4,9,2,2,6,8,7,5,3,
%U 4,5,8,8,2,4,8,1,0,9,7,6,9,2,8,9,2,8
%N Decimal expansion of Sum_{k>=0} (k+2) / (2k+1)!.
%F Equals (1/e + 4*sinh(1))/2.
%F Equals 2* 1F2(3;3/2,2;1/4) . - _R. J. Mathar_, Aug 02 2024
%e 2.53434210787332407456252558627193206403434152818407...
%t s = Sum[(k + 2)/(2 k + 1)!, {k, 0, Infinity}]
%t d = N[s, 100]
%t First[RealDigits[d]]
%Y Cf. A372389.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, May 12 2024