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A065955
a(n) = floor((-1)^n*n!*(E(n,2)-E(n,1)*E(n-1,1))) where E(n,x) = Sum_{k=0..n} (-1)^k*x^k/k!.
4
1, 1, 2, 3, 5, 8, 14, 26, 47, 86, 159, 295, 551, 1032, 1940, 3662, 6935, 13170, 25075, 47853, 91514, 175351, 336586, 647131, 1246069, 2402690, 4638908, 8967211, 17353537, 33618332, 65191862, 126535913, 245818070, 477938269, 929968028, 1810857390, 3528610689, 6880357955
OFFSET
0,3
EXAMPLE
1, 1, 2, 3, 5, 17/2, 89/6, 211/8, 1903/40, 62473/720, ...
MATHEMATICA
e[n_, x_]:=Sum[(-x)^k/k!, {k, 0, n}]; a[n_]:=Floor[(-1)^n*n!*(e[n, 2]-e[n, 1]e[n-1, 1])]; Array[a, 38, 0] (* Stefano Spezia, Apr 12 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 08 2001
EXTENSIONS
a(0)=1 prepended by and a(35)-a(37) from Stefano Spezia, Apr 12 2024
STATUS
approved