A193472 Numerator of ez(n-1)*n!/(4^n-2^n) where ez(n) is the n-th coefficient of sec(t)+tan(t) for n>0, a(0) = 1.
1, 1, 1, 3, 1, 25, 1, 427, 1, 12465, 5, 555731, 691, 35135945, 7, 2990414715, 3617, 329655706465, 43867, 45692713833379, 174611, 1111113564712575, 854513, 1595024111042171723, 236364091, 387863354088927172625, 8553103, 110350957750914345093747, 23749461029
Offset: 0
Links
- Peter Luschny, The lost Bernoulli numbers.
Programs
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Maple
gf := (f,n) -> coeff(series(f(x),x,n+1),x,n): BG := n ->`if`(n=0,1,gf(sec+tan,n-1)*n!/(4^n-2^n)): A193472 := n -> numer(BG(n)): seq(A193472(n),n=0..28);
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Mathematica
ez[n_] := SeriesCoefficient[Sec[t] + Tan[t], {t, 0, n}]; a[0] = 1; a[n_] := Numerator[ez[n-1] n!/(4^n - 2^n)]; Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Jun 24 2019 *)