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Search: id:A014307
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| A014307 |
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Expansion of sqrt( exp(x) / ( 2 - exp(x) )). |
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+0
6
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| 1, 1, 2, 7, 35, 226, 1787, 16717, 180560, 2211181, 30273047, 458186752, 7596317885, 136907048461, 2665084902482, 55726440112987, 1245661569161135, 29642264728189066, 748158516941653967, 19962900431638852297
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Tha Hankel transform of this sequence is A121835 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 31 2006
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REFERENCES
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M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.
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FORMULA
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Recurrence : a(n+1) = 1 + sum { j=1, n, (-1+binomial(n+1, j))*a(n) } - Jon Perry (perry(AT)globalnet.co.uk), Apr 25 2005
The Hankel transform of this sequence is A121835 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 31 2006
E.g.f. A(x) satisfies: A(x) = 1 + integral( A(x)^3 * exp(-x) ). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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PROGRAM
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(PARI) {a(n)=n!*polcoeff((exp(x +x*O(x^n))/(2-exp(x +x*O(x^n))))^(1/2), n)} (PARI) /* As solution to integral equation: */ {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+intformal(A^3*exp(-x+x*O(x^n)))); n!*polcoeff(A, n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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CROSSREFS
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Cf. A000110.
Cf. variants: A136727, A136728, A136729.
Sequence in context: A043546 A080831 A006947 this_sequence A000154 A003713 A058129
Adjacent sequences: A014304 A014305 A014306 this_sequence A014308 A014309 A014310
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KEYWORD
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nonn
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AUTHOR
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njas
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