OFFSET
1,2
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)!!.
EXAMPLE
a(4)=298 since 1/1+2/3+3/5+4/7=298/105=298/(7!!).
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Greg Huber, Apr 13 2020
STATUS
approved