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

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

Offset: 0

Author

Peter Luschny, Nov 08 2018

Keywords

• nonn

Comments

See A320956 for definitions and comments.

Examples

			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, ...
		

Crossrefs

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

A320959 (arctanh).

Cf. A177145, A001818, A122747.

Programs

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 *)