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A334066
a(n) = (2n-1)!!*(Sum_{k=1..n}k/(2*k-1)).
1
1, 5, 34, 298, 3207, 40947, 605076, 10157220, 190915965, 3971997585, 90613969110, 2249113016430, 60338869272675, 1739831420490975, 53656981894391400, 1762410972384203400, 61421841416041392825, 2263752327235180060125, 87970054921758957890250
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
Cf. A004041.
Sequence in context: A208677 A259906 A355258 * A330649 A121323 A362912
KEYWORD
nonn,easy
AUTHOR
Greg Huber, Apr 13 2020
STATUS
approved