A320958 The exponential limit of arcsin (odd indices only).

1, 5, 468, 197325, 233145675, 605979974250, 2987147975582925, 25254853526009732625, 340477692051264295027500, 6926101229658271208893970625, 203562520854789108487169894574375, 8346651541805126492397454664310896250, 463877742240727904202821053051014479795625

Offset

0,2

Comments

See A320956 for definitions and comments.

Links

Table of n, a(n) for n=0..12.

Example

Illustration of the convergence in the sense of A320956:
   [0] 0, 0, 0, 0, 0,   0, 0,      0, 0,         0, ...
   [1] 0, 1, 0, 1, 0,   9, 0,    225, 0,     11025, ... A177145, A001818
   [2] 0, 1, 0, 4, 0, 144, 0,  14400, 0,   2822400, ... A122747
   [3] 0, 1, 0, 5, 0, 369, 0,  82125, 0,  36173025, ...
   [4] 0, 1, 0, 5, 0, 459, 0, 160875, 0, 121837275, ...
   [5] 0, 1, 0, 5, 0, 468, 0, 192375, 0, 198472050, ...
   [6] 0, 1, 0, 5, 0, 468, 0, 197100, 0, 227644200, ...
   [7] 0, 1, 0, 5, 0, 468, 0, 197325, 0, 232737750, ...
   [8] 0, 1, 0, 5, 0, 468, 0, 197325, 0, 233134650, ...
   [9] 0, 1, 0, 5, 0, 468, 0, 197325, 0, 233145675, ...

Maple

# Function ExpLim defined in A320956.
L := [ExpLim(28, arcsin)]: seq(L[2*n], n=1..13);

Mathematica

m = 13; CoefficientList[ArcSin[x] + O[x]^(2 m + 1), x]*Range[0, 2 m - 1]!*BellB[Range[0, 2 m - 1]] // DeleteCases[#, 0]& (* Jean-François Alcover, Jul 23 2019 *)

Crossrefs

Cf. A320955 (exp), A320962 (log(x+1)), A320956 (sec+tan), this sequence (arcsin),

A320959 (arctanh).

Cf. A177145, A001818, A122747.

Sequence in context: A212043 A182403 A125534 * A262384 A024071 A321939

Adjacent sequences: A320955 A320956 A320957 * A320959 A320960 A320961

Keyword

nonn

Author

Peter Luschny, Nov 08 2018

Status

approved