A334066 a(n) = (2n-1)!!*(Sum_{k=1..n}k/(2*k-1)).

1, 5, 34, 298, 3207, 40947, 605076, 10157220, 190915965, 3971997585, 90613969110, 2249113016430, 60338869272675, 1739831420490975, 53656981894391400, 1762410972384203400, 61421841416041392825, 2263752327235180060125, 87970054921758957890250

Offset: 1

Author

Greg Huber, Apr 13 2020

Keywords

• nonn
• easy

Examples

			a(4)=298 since 1/1+2/3+3/5+4/7=298/105=298/(7!!).
		

Crossrefs

Cf. A004041.

Programs

Mathematica

Table[Sum[k/(2*k-1), {k, 1, n}], {n, 1, 19}]*Table[Product[2*j-1, {j, 1, n}], {n, 1, 19}]
FullSimplify[Table[(n/2 + HarmonicNumber[n - 1/2]/4 + Log[2]/2) * (2*n-1)!!, {n, 1, 20}]] (* Vaclav Kotesovec, Apr 14 2020 *)

Formula

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

Recurrence: a(n) = 2*a(n-1) + (2*n-3)^2*a(n-2) + (2*n-1)!!.