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A012521
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E.g.f.: arctanh(sinh(x)*exp(x)).
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0
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1, 2, 6, 32, 240, 2192, 23856, 303872, 4427520, 72545792, 1320608256, 26445350912, 577722163200, 13672510932992, 348466876717056, 9515645659185152, 277168473987809280, 8577847096804769792
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| E.g.f.: A(x) = arctanh(x) o x/(1-x) o tanh(x), a composition of functions involving tanh(x) and its inverse; thus, the n-th iteration of A(x) equals arctanh(x) o x/(1-n*x) o tanh(x). [From Paul D. Hanna, Nov 29 2011]
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EXAMPLE
| E.g.f.: x + 2/2!*x^2 + 6/3!*x^3 + 32/4!*x^4 + 240/5!*x^5 +...
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PROG
| (PARI){a(n)=n!*polcoeff(subst(atanh(x+x*O(x^n)), x, subst(x/(1-x), x, tanh(x+x*O(x^n)))), n)} /* Paul D. Hanna */
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CROSSREFS
| Sequence in context: A111550 A009686 A012318 * A012324 A121676 A133596
Adjacent sequences: A012518 A012519 A012520 * A012522 A012523 A012524
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KEYWORD
| nonn
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AUTHOR
| Patrick Demichel (dml(AT)hpfrcu03.france.hp.com)
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