A080094
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)=y(n).
Original entry on oeis.org
1, -3, 3, -1, 3, -5, -2, -5, 55, 106, 201, -2381, -7675, -35183, 145359, 910719, 8117231, 521487, -139498274, -2261959961, -7554900397, 17363594398, 690775844605, 4901767330647, 5460910088617, -179314430713387, -2668801066419061, -9075259309421889, -20645060784367893
Offset: 1
A080093
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).
Original entry on oeis.org
0, 1, 1, 2, 11, 41, 81, 715, 3425, 8861, 98253, 580317, 1816640, 24011157, 166888165, 608035190, 9264071767, 73600798037, 304238004061, 5224266196935, 46499892038437, 214184962059157, 4078345814329009, 40073660040755337
Offset: 1
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...
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