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A012136 Expansion of e.g.f. tan(arcsin(arctanh(x))) (odd powers only). 0

%I

%S 1,5,129,7797,848481,145041093,35799178401,12045448529397,

%T 5298881528389185,2952169020073027845,2031522244065649876545,

%U 1692164698229362361298165,1677876856826199251515980705

%N Expansion of e.g.f. tan(arcsin(arctanh(x))) (odd powers only).

%F a(n) = (2*n+1)!*sum(k=0..n, 16^(-k)*binomial(2*k,k)*(2*k+1)!*sum(i=2*k+1..2*n+1, (2^i*Stirling1(i,2*k+1)*binomial(2*n,i-1))/i!))/2. - _Vladimir Kruchinin_, Jun 17 2011

%e tan(arcsin(arctanh(x))) = x + (5/3!)*x^3 + (129/5)!*x^5 + (7797/7!)*x^7 + (848481/9!)*x^9 + ...

%o (Maxima)

%o a(n):=(2*n+1)!*sum(16^(-k)*binomial(2*k,k)*(2*k+1)!*sum((2^i*stirling1(i,2*k+1)*binomial(2*n,i-1))/i!,i,2*k+1,2*n+1),k,0,n)/2; /* _Vladimir Kruchinin_, Jun 17 2011 */

%K nonn

%O 1,2

%A Patrick Demichel (patrick.demichel(AT)hp.com)

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Last modified August 3 08:53 EDT 2020. Contains 336197 sequences. (Running on oeis4.)