A080093 - OEIS

%I #7 Mar 30 2012 18:39:15

%S 0,1,1,2,11,41,81,715,3425,8861,98253,580317,1816640,24011157,

%T 166888165,608035190,9264071767,73600798037,304238004061,

%U 5224266196935,46499892038437,214184962059157,4078345814329009,40073660040755337

%N Let sum(k>=0, k^n/(2*k+1)!) = (x(n)*e + y(n)/e)/z(n), where x(n) and z(n) are >0, then a(n)=x(n).

%e Values of sum(k>=0,k^n/(2*k+1)!) = (x(n)*e + y(n)/e)/z(n) are given by n=1: (1/e)/2 = 0.183939720585721160..., n=2: (e - 3/e)/8 = 0.201830438118089783..., n=3: (e + 3/e)/16 = 0.238870009498335762..., n=4: (2e - 1/e)/16 = 0.316792763484165509..., n=5: (11e + 3/e)/64 = 0.484449038071309758..., n=6: (41e - 5/e)/128 = 0.856329357507528461..., n=7: (81e - 2/e)/128 = 1.71441460330343577..., n=8: (715e - 5/e)/512 = 3.79244552762179713..., n=9: (3425e + 55/e)/1024 = 9.11166858568033130..., n=10: (8861e + 106/e)/1024 = 23.5602446315818092...

%Y Cf. A080094, A080095, A079750 - A079756.

%K nonn

%O 1,4

%A _Benoit Cloitre_ and _Paul D. Hanna_, Jan 28 2003