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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

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

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-Fran├žois Alcover, Oct 02 2012 *)

CROSSREFS

Cf. A191302, A191754, A181131.

Sequence in context: A019013 A165422 A051460 * A101407 A294245 A117785

Adjacent sequences:  A191969 A191970 A191971 * A191973 A191974 A191975

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 August 20 07:48 EDT 2019. Contains 326143 sequences. (Running on oeis4.)