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A012113
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E.g.f. tan(arcsin(arcsinh(x))) (odd powers only).
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0
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1, 2, 24, 552, 28032, 1778688, 212383872, 25215328512, 5734229114880, 1029078328135680, 410202091438571520, 93624495716395745280, 65377722614151010222080, 15441784659337549573324800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n)=((2*n+1)!*sum(m=0..n, binomial(2*m,m)*2^(-2*m)*(2*m+1)!*(sum(j=0..n-m, (-1)^(n-m+j)*(sum(i=0..2*j,(2^i*stirling1(2*m+1+i,2*m+1)* binomial(2*m+2*j,2*m+i))/(2*m+1+i)!)) *binomial(n-1/2,n-m-j))))). [From Vladimir Kruchinin, Jun 17 2011]
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EXAMPLE
| tan(arcsin(arcsinh(x)))=x+2/3!*x^3+24/5!*x^5+552/7!*x^7+28032/9!*x^9...
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PROG
| (Maxima)
a(n):=((2*n+1)!*sum(binomial(2*m, m)*2^(-2*m)*(2*m+1)!*(sum((-1)^(n-m+j)*(sum((2^i*stirling1(2*m+1+i, 2*m+1)*binomial(2*m+2*j, 2*m+i))/(2*m+1+i)!, i, 0, 2*j))*binomial(n-1/2, n-m-j), j, 0, n-m)), m, 0, n)); [From Vladimir Kruchinin, Jun 17 2011]
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CROSSREFS
| Sequence in context: A054946 A046744 A000186 * A156525 A170904 A090732
Adjacent sequences: A012110 A012111 A012112 * A012114 A012115 A012116
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KEYWORD
| nonn
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AUTHOR
| Patrick Demichel (dml(AT)hpfrcu03.france.hp.com)
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