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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

Table of n, a(n) for n=0..29.

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.)