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%I #18 Apr 30 2020 02:23:16
%S 1,5,34,298,3207,40947,605076,10157220,190915965,3971997585,
%T 90613969110,2249113016430,60338869272675,1739831420490975,
%U 53656981894391400,1762410972384203400,61421841416041392825,2263752327235180060125,87970054921758957890250
%N a(n) = (2n-1)!!*(Sum_{k=1..n}k/(2*k-1)).
%F a(n) = (2n-1)!!*(Sum_{k=1..n}k/(2*k-1)).
%F Recurrence: a(n) = 2*a(n-1) + (2*n-3)^2*a(n-2) + (2*n-1)!!.
%e a(4)=298 since 1/1+2/3+3/5+4/7=298/105=298/(7!!).
%t Table[Sum[k/(2*k-1), {k, 1, n}], {n, 1, 19}]*Table[Product[2*j-1, {j, 1, n}], {n, 1, 19}]
%t FullSimplify[Table[(n/2 + HarmonicNumber[n - 1/2]/4 + Log[2]/2) * (2*n-1)!!, {n, 1, 20}]] (* _Vaclav Kotesovec_, Apr 14 2020 *)
%Y Cf. A004041.
%K nonn,easy
%O 1,2
%A _Greg Huber_, Apr 13 2020
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