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 A193476 The denominators of the Bernoulli secant numbers at odd indices. 1
 2, 56, 992, 16256, 261632, 4192256, 67100672, 1073709056, 17179738112, 274877382656, 628292059136, 70368735789056, 1125899873288192, 18014398375264256, 288230375614840832, 4611686016279904256, 73786976286248271872, 1180591620683051565056 (list; graph; refs; listen; history; text; internal format)
 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 A009843. A193475(n) = 4*16^n-2*4^n is similar, but differs at n = 10, 31, 52, 73, 77, 94, ... LINKS Peter Luschny, The lost Bernoulli numbers. MAPLE gf := (f, n) -> coeff(series(f(x), x, n+4), x, n): A193476 := n -> denom(gf(sec+tan, 2*n)*(2*n+1)!/(4*16^n - 2*4^n)): seq(A193476(n), n = 0..17); 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 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, A009843, 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

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Last modified January 28 22:35 EST 2020. Contains 331328 sequences. (Running on oeis4.)