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 A165161 Numerator of the n-th term in the first differences of the binomial transform of the "original" Bernoulli numbers. 2
 1, 2, 5, 29, 31, 43, 41, 29, 31, 71, 61, 2039, 3421, 13, -1, -3107, 4127, 44665, -43069, -174281, 174941, 854651, -854375, -236361361, 236366821, 8553109, -8553097, -23749460159, 23749461899, 8615841290327 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The binomial transform of the "original" Bernoulli numbers is 1, 3/2, 13/6, ... as mentioned in A164558. The first differences of that sequence are 3/2 - 1 = 1/2, 13/6 - 3/2 = 2/3, 5/6, 29/30, 31/30, ... and the numerators of these differences are listed here. The bisection a(2n) reappears (up to signs) as A162173(n+1). LINKS FORMULA a(2n) + A000367(n) = A006954(n+1) = A051717(2n+1). a(2n+1) + a(2n+2) = A051717(2n+2) + A051717(2n+3), n > 0. MAPLE read("transforms") : A164555 := proc(n) if n <= 2 then 1; else numer(bernoulli(n)) ; end if; end proc: A027642 := proc(n) denom(bernoulli(n)) ; end proc: nmax := 40: BINOMIAL([seq(A164555(n)/A027642(n), n=0..nmax)]) : map(numer, DIFF(%)) ; # R. J. Mathar, Jul 07 2011 CROSSREFS Cf. A051717 (denominators), A164555, A027642. Sequence in context: A327345 A049050 A178322 * A098858 A213995 A134449 Adjacent sequences:  A165158 A165159 A165160 * A165162 A165163 A165164 KEYWORD frac,sign AUTHOR Paul Curtz, Sep 06 2009 STATUS approved

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Last modified January 20 13:55 EST 2022. Contains 350472 sequences. (Running on oeis4.)