A193476 The denominators of the Bernoulli secant numbers at odd indices.

2, 56, 992, 16256, 261632, 4192256, 67100672, 1073709056, 17179738112, 274877382656, 628292059136, 70368735789056, 1125899873288192, 18014398375264256, 288230375614840832, 4611686016279904256, 73786976286248271872, 1180591620683051565056

Offset

0,1

Comments

Denominator of the coefficient [x^(2n)] of sec(x)*(2*n+1)!/(4*16^n-2*4^n), that is, a(n) is the denominator of A000364(n)*(2*n+1)/(4*16^n-2*4^n). [Edited by Altug Alkan, Apr 22 2018]

Numerators are A160143. [Corrected by Peter Luschny, Mar 18 2021]

A193475(n) = 4*16^n-2*4^n is similar, but differs at n = 10, 31, 52, 73, 77, 94, ...

Links

Table of n, a(n) for n=0..17.

Peter Luschny, The lost Bernoulli numbers.

Maple

gf := (f, n) -> coeff(series(f(x), x, n+4), x, n):
A193476 := n -> denom(gf(sec, 2*n)*(2*n+1)!/(4*16^n - 2*4^n)):
seq(A193476(n), n = 0..17); # Altug Alkan, Apr 23 2018

Mathematica

a[n_] := Sum[Sum[Binomial[k, m] (-1)^(n+k)/(2^(m-1)) Sum[Binomial[m, j]*(2j - m)^(2n), {j, 0, m/2}]*(-1)^(k-m), {m, 0, k}], {k, 1, 2n}] (2n+1)/ (4*16^n - 2*4^n) // Denominator; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Jun 26 2019, after Vladimir Kruchinin in A000364 *)

Prog

(PARI) a(n) = denominator(subst(bernpol(2*n+1), 'x, 1/4)*2^(2*n+1)/(2^(2*n+1)-1)); \\ Altug Alkan, Apr 22 2018 after Charles R Greathouse IV at A000364

Crossrefs

Cf. A000364, A160143, A160144, A193475.

Sequence in context: A080313 A080268 A224297 * A193475 A246001 A009555

Adjacent sequences: A193473 A193474 A193475 * A193477 A193478 A193479

Keyword

nonn,frac

Author

Peter Luschny, Aug 17 2011

Status

approved