A259239 E.g.f.: exp(x-sqrt(1-x^2)+1).

1, 1, 2, 4, 13, 41, 211, 967, 7274, 44578, 449551, 3456641, 43883797, 405589549, 6212792678, 67022223556, 1202604514141, 14825243365517, 304950638503279, 4227716923246963, 98067246206824406, 1509933505953992386, 38990856819985996927, 660048542856323263589, 18778057160849966289433

Offset: 0

Author

Karol A. Penson, Jun 22 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Programs

Maple

a:= proc(n) option remember; `if`(n<4, [1$2, 2, 4][n+1],
      ((2*n-3)*a(n-1) +(n-1)*(n^2-5*n+5)*a(n-2)
       +2*(n-1)*(n-2)*(n-3)*(a(n-4)-a(n-3)))/(n-2))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Jun 22 2015

Mathematica

CoefficientList[Series[E^(x-Sqrt[1-x^2]+1), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jun 22 2015 *)

Formula

a(n) ~ (exp(2) + (-1)^n) * n^(n-1) / exp(n). - Vaclav Kotesovec, Jun 22 2015

a(n) = ((2*n-3)*a(n-1) + (n-1)*(n^2-5*n+5)*a(n-2) + 2*(n-1)*(n-2)*(n-3)*(a(n-4)-a(n-3)))/(n-2) for n >= 4. - Alois P. Heinz, Jan 30 2020