A178345 a(n)= 2^A006218(n)/( (n!)^2 *sum_{m=0..n} 1/(m!*(2n-m+1)!) ) .

1, 3, 15, 70, 630, 2772, 48048, 205920, 3500640, 29560960, 496624128, 2076791808, 138452787200, 575111577600, 9530420428800, 157569617756160, 5199797385953280, 21410930412748800, 1408363422705254400

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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).

Maple

A006218 := proc(n) add( floor(n/i), i=1..n) ; end proc:
A178345 := proc(n) n!^2*add( 1/(2*n-m+1)!/m!, m=0..n) ; 2^A006218(n)/% ; end proc:
seq(A178345(n), n=0..10) ;

Mathematica

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}]));
Table[a[n], {n, 0, 20}]

Crossrefs

Cf. A001803.

Sequence in context: A291031 A359405 A009174 * A183547 A123942 A357161

Adjacent sequences: A178342 A178343 A178344 * A178346 A178347 A178348

Keyword

nonn

Author

Roger L. Bagula, May 25 2010

Status

approved