A165299 a(n) = A002790(n) / A164020(n).
1, 1, 1, 1, 1, 2, 2, 3, 3, 2, 2, 2, 2, 60, 60, 1, 3, 10, 10, 42, 42, 20, 12, 30, 30, 252, 36, 4, 4, 8, 8, 231, 231, 70, 210, 2, 2, 5460, 5460, 14, 42, 660, 132, 1260, 1260, 56, 840, 210, 210, 7956, 7956, 44, 396, 440, 440, 228, 228, 40, 120, 24, 24, 720720, 144144, 715, 2145, 102, 510
Offset: 0
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Maple
A002790 := proc(n) add((-1)^k*stirling1(n, k)/(k+1), k=0..n) ; denom(%) ; end proc: A002445 := proc(n) bernoulli(2*n) ; denom(%) ; end proc: A164020 := proc(n) if type(n,'even') then A002445(n/2) ; else n+1 ; end if; end proc: A165299 := proc(n) A002790(n)/A164020(n) ; end proc: seq(A165299(n),n=0..80) ; # R. J. Mathar, Jul 04 2011