A295098 a(n) = n! * [x^n] exp(n*x)*(1 + exp(x^2/2)*x*(1 + sqrt(Pi/2)*erf(x/sqrt(2)))).
1, 2, 10, 75, 760, 9715, 150060, 2719017, 56556480, 1328337117, 34773226340, 1003998156293, 31696623421488, 1086258754644505, 40161805428662876, 1593475984997421525, 67534151717002711296, 3044989873158805787409, 145537456143562934305860, 7350253384336351186239341, 391132792671917087054081200
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..250
- N. J. A. Sloane, Transforms
- Index entries for sequences related to factorial numbers
Programs
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Mathematica
Table[n! SeriesCoefficient[Exp[n x] (1 + Exp[x^2/2] x (1 + Sqrt[Pi/2] Erf[x/Sqrt[2]])), {x, 0, n}], {n, 0, 20}]
Formula
a(n) ~ c * n^n, where c = 1 + exp(1/2) * (1 + sqrt(Pi/2) * erf(1/sqrt(2))) = 4.0594074053425761445394754992332... - Vaclav Kotesovec, Aug 21 2018
Comments