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 A178345 a(n)= 2^A006218(n)/( (n!)^2 *sum_{m=0..n} 1/(m!*(2n-m+1)!) ) . 1
 1, 3, 15, 70, 630, 2772, 48048, 205920, 3500640, 29560960, 496624128, 2076791808, 138452787200, 575111577600, 9530420428800, 157569617756160, 5199797385953280, 21410930412748800, 1408363422705254400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS 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: A033876 A291031 A009174 * A183547 A123942 A290902 Adjacent sequences:  A178342 A178343 A178344 * A178346 A178347 A178348 KEYWORD nonn AUTHOR Roger L. Bagula, May 25 2010 STATUS approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)