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%I #14 Jul 31 2023 10:54:57
%S 3,-9,69,-531,6147,-73665,1143045,-18456795,359420355,-7279744185,
%T 170639259525,-4151789871075,113815089771075,-3231091019581425,
%U 101428235414230725,-3289812808335928875,116369085609950047875,-4244245621899589931625,167038144384492533277125
%N a(2,n) as defined in A003148.
%F Conjecture: a(n) + 3*a(n-1) - 2*(2*n+3)*(n-1)*a(n-2) = 0. - _R. J. Mathar_, Mar 12 2013
%p A003148 := proc(m::integer,n::integer) RETURN( doublefactorial(2*n+2*m+1)/(2*m+1)*simplify(hypergeom([ -n,m+1/2],[m+3/2],2))) ; end:
%p A084543 := proc(n::integer) RETURN(A003148(2,n)) ; end:
%p for n from 0 to 20 do print(A084543(n)); od: # _R. J. Mathar_, Apr 25 2006
%t a[m_, n_] := (2n + 2m + 1)!!/(2m + 1)*Hypergeometric2F1[-n, m + 1/2, m + 3/2, 2];
%t Table[a[2, n], {n, 0, 20}] (* _Jean-François Alcover_, Jul 31 2023, after _R. J. Mathar_ *)
%K sign
%O 0,1
%A _R. J. Mathar_, Jul 01 2003
%E More terms from _R. J. Mathar_, Apr 25 2006
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