A334000 a(n) = (2*n+1)!! * Sum_{k=0..n} k/(2*k+1).

0, 1, 11, 122, 1518, 21423, 340869, 6058980, 119218860, 2575293165, 60628447215, 1545696702270, 42437227275450, 1248581232985275, 39197268410049225, 1307969571015966600, 46233376386927067800, 1725823391345415833625, 67845041198360981737875

Offset: 0

Author

Greg Huber, Apr 11 2020

Keywords

• nonn
• easy

Examples

			a(3) = 122 since 0/1 + 1/3 + 2/5 + 3/7 = 122/105 = 122/(7!!).
		

Crossrefs

Cf. A004041.

Programs

Mathematica

Table[Sum[k/(2*k+1),{k,0,n}],{n,0,18}]*Table[Product[2*j+1,{j,0,n}],{n,0,18}]
FullSimplify[Table[((n+1)/2 - HarmonicNumber[n + 1/2]/4 - Log[2]/2) * (2*n+1)!!, {n, 0, 20}]] (* Vaclav Kotesovec, Apr 14 2020 *)

Formula

a(n) = (2*n+1)!!*(Sum_{k=0..n} k/(2*k+1)).

Recurrence: a(n) = 4*n*a(n-1)-(2*n-1)^2*a(n-2)+(2*n-1)!!.