A193473 Denominator 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, 2, 6, 56, 30, 992, 42, 16256, 30, 261632, 66, 4192256, 2730, 67100672, 6, 1073709056, 510, 17179738112, 798, 274877382656, 330, 628292059136, 138, 70368735789056, 2730, 1125899873288192, 6, 18014398375264256, 870

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Peter Luschny, The lost Bernoulli numbers.

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)):
A193473 := n -> denom(BG(n)): seq(A193473(n), n=0..28);

Mathematica

ez[n_] := SeriesCoefficient[Sec[t] + Tan[t], {t, 0, n}];
a[0] = 1; a[n_] := Denominator[ez[n - 1] n!/(4^n - 2^n)];
Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Jun 26 2019 *)

Crossrefs

Cf. A000367, A002445, A009843, A193475, A193472.

Sequence in context: A153450 A179389 A084123 * A336899 A181509 A213026

Adjacent sequences: A193470 A193471 A193472 * A193474 A193475 A193476

Keyword

nonn,frac

Author

Peter Luschny, Aug 07 2011

Status

approved