A163168 Pierce expansion of sech(1).

1, 2, 3, 8, 9, 24, 37, 85, 1115, 29153, 423233, 2208087, 5102497, 9813637, 15922076, 19204759, 106559540, 120015709, 1493877142, 2199074984, 32818755269, 1505298832166, 1507229768977, 2841536357911, 14805574584765

Offset: 1

Author

R. J. Mathar, Jul 22 2009

Keywords

• nonn

Comments

Pierce expansion of A073746.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Eric Weisstein, Pierce Expansion, Mathworld.

Programs

Mathematica

PierceExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@ NestList[{Floor[1/Expand[1 - #[[1]] #[[2]]]], Expand[1 - #[[1]] #[[2]]]} &, {Floor[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; PierceExp[N[Sech[1] , 7!], 50] (* G. C. Greubel, Nov 14 2016 *)

Formula

0.648054... = 1/1 - 1/(1*2) + 1/(1*2*3) - 1/(1*2*3*8) + 1/(1*2*3*8*9) - ...