A191972 - OEIS

%I #17 Feb 24 2019 04:32:11

%S 1,-1,1,-4,4,-16,3056,-1856,181312,-35853056,1670556928,-39832634368,

%T 545273832448,-19385421824,53026545299456,-2753673793480966144,

%U 68423881271489019904,-22654998127210332160

%N 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.

%C For the denominators of T(n, n+1) see A190339, where detailed information can be found.

%F T(n, n+1) = T(n, n)/2.

%F a(n+2) = (-1)^n*A181130(n+2)/2.

%e T(n,n+1) = [1/2, -1/6, 1/15 , -4/105, 4/105, -16/231, 3056/15015, -1856/2145, 181312/36465, ...]

%p 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

%t 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 *)

%Y Cf. A191302, A191754, A181131.

%K sign,frac

%O 0,4

%A _Paul Curtz_, Jun 20 2011

%E Thanks to _R. J. Mathar_ by _Paul Curtz_, Jun 20 2011

%E Edited by _Johannes W. Meijer_, Jun 30 2011