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%I #24 Jun 09 2014 17:49:03
%S 1,-1,-4,-1,-8,-1,-8,-3,-8,1,104,-41,-920,1767,20168,-8317,-2022392,
%T 869807,291391192,-129169263,-2759924456,250158593,146772324808,
%U -67632514765,-10164962436952
%N Define a square array B(m,n) (m>=0, n>=0) by B(n, n) = A212196(n)/A181131(n), B(n, n+1) = -A212196(n)/A181131(n), B(m, n) = B(m, n-1) + B(m+1, n-1); a(n) = numerator of B(0,n).
%C The array B(m,n) begins:
%C 1, -1, -4/3, -1, -8/15, -1/5, -8/105,...
%C -2, -1/3, 1/3, 7/15, 1/3, 13/105,...
%C 5/3, 2/3, 2/15, -2/15, -22/105,...
%C -1, -8/15, -4/15, -8/105,...
%C 7/15, 4/15, 4/21,...
%C -1/5, -8/105,...
%C 13/105,...
%C etc.
%C B(0, n) = 1, -1, -4/3, -1, -8/15, -1/5, -8/105, -3/35, -8/105, 1/35, 104/1155, ... = a(n)/b(n).
%C The main diagonal is A212196(n)/A181131(n).
%C The first upper diagonal is -A212196(n)/A181131(n).
%t max = 12; t[0] = Table[BernoulliB[n], {n, 0, 2*max}]; t[n_] := t[n] = Differences[t[0], n]; B1[1, 1] = -1/3; B1[n_, n_] := t[n][[n+1]]; B1[m_, n_] /; n == m+1 := B1[m, n] = -B1[m, m]; B1[m_?NonNegative, n_?NonNegative] := B1[m, n] = B1[m, n-1] + B1[m+1, n-1]; B1[_, _] = 0; Table[B1[0, n] // Numerator, {n, 0, 2*max}] (* _Jean-François Alcover_, Apr 14 2014 *)
%K sign,frac
%O 0,3
%A _Paul Curtz_, Apr 12 2014
%E More terms from _Jean-François Alcover_, Apr 14 2014
%E Edited by _N. J. A. Sloane_, May 21 2014