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1, 1, 1, 2, 5, 20, 85, 520, 3145, 26000, 204425, 2132000, 20646925, 260104000, 2993804125, 44217680000, 589779412625, 9993195680000, 151573309044625, 2898026747200000, 49261325439503125, 1049085682486400000, 19753791501240753125, 463695871658988800000

a:= n-> n!*coeff(series(exp(arcsin(x)), x, n+1), x, n):

seq(a(n), n=0..25); # Alois P. Heinz, Aug 17 2018

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T. D. Noe, <a href="/A006228/b006228.txt">Table of n, a(n) for n = 0..100</a>

i even: a_i = Prod_Product_{j=1..i/2-1} 1 + 4j^2, i odd: a_i = Prod_Product_{j=1..(i-1)/2} 2 + 4j(j-1). - Cris Moore (moore(AT)santafe.edu), Jan 31 2001

a(0)=1, a(1)=1, a(n) = (1+(n-2)^2)*a(n-2) for n >= 2. Jaume Oliver Lafont, Oct 24 2009

Bisections are expansions of sin(asinharcsinh(x)) and cos(asinharcsinh(x)).

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Kruchinin Vladimir Victorovich, <a href="http://arxiv.org/abs/1009.2565">Composition of ordinary generating functions</a>, arXiv:1009.2565 [math.CO], 2010.

i even: a_i = prod_Prod_{j=1}^{..i/2-1} 1 + 4j^2, i odd: a_i = prod_Prod_{j=1}^{..(i-1)/2} 2 + 4j(j-1). - Cris Moore (moore(AT)santafe.edu), Jan 31 2001

a(0)=1, a(1)=1, a(n) = (1+(n-2)^2)*a(n-2) for n>=2. Jaume Oliver Lafont, Oct 24 2009

(Maxima) a(n):=(n-1)!*sum((if n=m then 1 else if oddp(n-m) then 0 else sum((-1)^k*(sum(binomial(k, j)*2^(1-j)*sum((-1)^((n-m)/2-i)*binomial(j, i)*(j-2*i)^(n-m+j)/(n-m+j)!, i, 0, floor(j/2))*(-1)^(k-j), j, 1, k))*binomial(k+n-1, n-1), k, 1, n-m))/(m-1)!, m, 1, n); [_/* _Vladimir Kruchinin_, Sep 12 2010] */

H. S. Uhler, On the numerical value of i^i, Amer. Math. Monthly, 28 (1921), 114-116.

H. S. Uhler, <a href="http://www.jstor.org/stable/2972387">On the numerical value of i^i</a>, Amer. Math. Monthly, 28 (1921), 114-116.

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Expansion of exp(arcsin (x)).