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Search: id:A082579
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| 1, 1, 5, 31, 241, 2261, 24781, 309835, 4342241, 67308841, 1141960501, 21026890391, 417264626065, 8871853115581, 201100863674621, 4838817223845571, 123128720142540481, 3302478863343928145, 93091427773284348901
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OFFSET
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0,3
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FORMULA
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a(n) = Sum[ Binomial[ n + k - 1, 2 k - 1 ] n! / k!, { k, 1, n } ]. Recurrence: a(n+3) - ( 3 n + 7 ) a(n+2) + ( n + 2 )( 3 n + 2 ) a(n+1) - ( n + 2 )( n + 1 ) n a(n) = 0. E.g.f.:: Exp[ x/( 1 - x )^2 ]
Special values of the hypergeometric function 2F2 : a(n)=n!*n*hypergeom([n+1, -n+1], [3/2, 2], -1/4), n=1, 2... . From Karol A. Penson - (penson(AT)lptl.jussieu.fr)- Jan 29 04.
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CROSSREFS
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Sequence in context: A052773 A062147 A069321 this_sequence A024451 A046852 A056541
Adjacent sequences: A082576 A082577 A082578 this_sequence A082580 A082581 A082582
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KEYWORD
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easy,nonn
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AUTHOR
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Emanuele Munarini (munarini(AT)mate.polimi.it), May 07 2003
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