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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 Cf. A191302, A191754, A181131. Sequence in context: A340425 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 September 24 16:35 EDT 2021. Contains 347651 sequences. (Running on oeis4.)