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A320958 The exponential limit of arcsin (odd indices only). 4

%I #10 Jul 23 2019 04:27:01

%S 1,5,468,197325,233145675,605979974250,2987147975582925,

%T 25254853526009732625,340477692051264295027500,

%U 6926101229658271208893970625,203562520854789108487169894574375,8346651541805126492397454664310896250,463877742240727904202821053051014479795625

%N The exponential limit of arcsin (odd indices only).

%C See A320956 for definitions and comments.

%e Illustration of the convergence in the sense of A320956:

%e [0] 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e [1] 0, 1, 0, 1, 0, 9, 0, 225, 0, 11025, ... A177145, A001818

%e [2] 0, 1, 0, 4, 0, 144, 0, 14400, 0, 2822400, ... A122747

%e [3] 0, 1, 0, 5, 0, 369, 0, 82125, 0, 36173025, ...

%e [4] 0, 1, 0, 5, 0, 459, 0, 160875, 0, 121837275, ...

%e [5] 0, 1, 0, 5, 0, 468, 0, 192375, 0, 198472050, ...

%e [6] 0, 1, 0, 5, 0, 468, 0, 197100, 0, 227644200, ...

%e [7] 0, 1, 0, 5, 0, 468, 0, 197325, 0, 232737750, ...

%e [8] 0, 1, 0, 5, 0, 468, 0, 197325, 0, 233134650, ...

%e [9] 0, 1, 0, 5, 0, 468, 0, 197325, 0, 233145675, ...

%p # Function ExpLim defined in A320956.

%p L := [ExpLim(28, arcsin)]: seq(L[2*n], n=1..13);

%t 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 *)

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

%Y A320959 (arctanh).

%Y Cf. A177145, A001818, A122747.

%K nonn

%O 0,2

%A _Peter Luschny_, Nov 08 2018

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)