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A191972 The numerators of T(n, n+1) with T(0, m) = A164555(m)/A027642(m) and T(n, m) = T(n-1, m+1) - T(n-1, m), n >= 1, m >= 0. 1
1, -1, 1, -4, 4, -16, 3056, -1856, 181312, -35853056, 1670556928, -39832634368, 545273832448, -19385421824, 53026545299456, -2753673793480966144, 68423881271489019904, -22654998127210332160 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
For the denominators of T(n, n+1) see A190339, where detailed information can be found.
LINKS
FORMULA
T(n, n+1) = T(n, n)/2.
a(n+2) = (-1)^n*A181130(n+2)/2.
EXAMPLE
T(n,n+1) = [1/2, -1/6, 1/15 , -4/105, 4/105, -16/231, 3056/15015, -1856/2145, 181312/36465, ...]
MAPLE
nmax:=20: mmax:=nmax: A164555:=proc(n): if n=1 then 1 else numer(bernoulli(n)) fi: end: A027642:=proc(n): if n=1 then 2 else denom(bernoulli(n)) fi: end: for m from 0 to 2*mmax do T(0, m):=A164555(m)/A027642(m) od: for n from 1 to nmax do for m from 0 to 2*mmax do T(n, m):=T(n-1, m+1)-T(n-1, m) od: od: for n from 0 to nmax do seq(T(n, m), m=0..mmax) od: seq(numer(T(n, n+1)), n=0..nmax-1); # Johannes W. Meijer, Jun 30 2011
MATHEMATICA
nmax = 17; b[n_] := BernoulliB[n]; b[1] = 1/2; bb = Table[b[n], {n, 0, 2*nmax+1}]; dd = Table[Differences[bb, n], {n, 1, nmax }]; a[0] = 1; a[n_] := dd[[n, n+2]] // Numerator; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Oct 02 2012 *)
CROSSREFS
Sequence in context: A340425 A165422 A051460 * A101407 A294245 A117785
KEYWORD
sign,frac
AUTHOR
Paul Curtz, Jun 20 2011
EXTENSIONS
Thanks to R. J. Mathar by Paul Curtz, Jun 20 2011
Edited by Johannes W. Meijer, Jun 30 2011
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)