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A240776 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).

%I A240776 #24 Jun 09 2014 17:49:03
%S A240776 1,-1,-4,-1,-8,-1,-8,-3,-8,1,104,-41,-920,1767,20168,-8317,-2022392,
%T A240776 869807,291391192,-129169263,-2759924456,250158593,146772324808,
%U A240776 -67632514765,-10164962436952
%N A240776 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 A240776 The array B(m,n) begins:
%C A240776 1,          -1,  -4/3,     -1,   -8/15,   -1/5, -8/105,...
%C A240776 -2,       -1/3,   1/3,   7/15,     1/3, 13/105,...
%C A240776 5/3,       2/3,  2/15,  -2/15, -22/105,...
%C A240776 -1,      -8/15, -4/15, -8/105,...
%C A240776 7/15,     4/15,  4/21,...
%C A240776 -1/5,   -8/105,...
%C A240776 13/105,...
%C A240776 etc.
%C A240776 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 A240776 The main diagonal is A212196(n)/A181131(n).
%C A240776 The first upper diagonal is -A212196(n)/A181131(n).
%t A240776 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 A240776 sign,frac
%O A240776 0,3
%A A240776 _Paul Curtz_, Apr 12 2014
%E A240776 More terms from _Jean-François Alcover_, Apr 14 2014
%E A240776 Edited by _N. J. A. Sloane_, May 21 2014