A178345 - OEIS

%I #5 Mar 30 2012 17:34:41

%S 1,3,15,70,630,2772,48048,205920,3500640,29560960,496624128,

%T 2076791808,138452787200,575111577600,9530420428800,157569617756160,

%U 5199797385953280,21410930412748800,1408363422705254400

%N a(n)= 2^A006218(n)/( (n!)^2 *sum_{m=0..n} 1/(m!*(2n-m+1)!) ) .

%F a(n)= 2^A006218(n)/sum_{m=0..n} Beta(n+1,n-m+1)*binomial(n,m) ) , where Beta(x,y)= Gamma(x)*Gamma(y)/Gamma(x+y).

%p A006218 := proc(n) add( floor(n/i),i=1..n) ; end proc:

%p A178345 := proc(n) n!^2*add( 1/(2*n-m+1)!/m!,m=0..n) ; 2^A006218(n)/% ; end proc:

%p seq(A178345(n),n=0..10) ;

%t a[n_] = 1/(Sum[Beta[ n + 1, n - m + 1]*Binomial[n, m], {m, 0, n}]*(1/2)^(Sum[ Floor[n/i], {i, 1, n}]));

%t Table[a[n], {n, 0, 20}]

%Y Cf. A001803.

%K nonn

%O 0,2

%A _Roger L. Bagula_, May 25 2010