%I A082579
%S A082579 1,1,5,31,241,2261,24781,309835,4342241,67308841,1141960501,21026890391,
%T A082579 417264626065,8871853115581,201100863674621,4838817223845571,
%U A082579 123128720142540481,3302478863343928145,93091427773284348901
%N A082579 A binomial sum.
%F A082579 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 ]
%F A082579 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.
%Y A082579 Sequence in context: A052773 A062147 A069321 this_sequence A024451 A046852 
               A056541
%Y A082579 Adjacent sequences: A082576 A082577 A082578 this_sequence A082580 A082581 
               A082582
%K A082579 easy,nonn
%O A082579 0,3
%A A082579 Emanuele Munarini (munarini(AT)mate.polimi.it), May 07 2003