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

Author

Peter Luschny, Aug 07 2011

Keywords

• nonn
• frac

Links

• Peter Luschny, The lost Bernoulli numbers.

Crossrefs

Cf. A000367, A002445, A009843, A193475, A193473.

Programs

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);

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 *)