cp's OEIS Frontend

A230324 a(n) = A226158(n) - 2*A226158(n+1).

%I A230324 #22 Jan 19 2018 19:35:24
%S A230324 2,1,-1,-2,1,6,-3,-34,17,310,-155,-4146,2073,76454,-38227,-1859138,
%T A230324 929569,57641238,-28820619,-2219305810,1109652905,103886563462,
%U A230324 -51943281731,-5810302084962,2905151042481,382659344967926
%N A230324 a(n) = A226158(n) - 2*A226158(n+1).
%C A230324 The array A(n,k) = A(n-1,k+1) - A(n-1,k) of the sequence in the first row and higher-order sequences in followup rows starts:
%C A230324    2,  1,  -1,   -2,     1,     6,    -3, ...
%C A230324   -1, -2,  -1,    3,     5,    -9,   -31, ...
%C A230324   -1,  1,   4,    2,   -14,   -22,    82, ...
%C A230324    2,  3,  -2,  -16,    -8,   104,   160, ...
%C A230324    1, -5, -14,    8,   112,    56, -1160, ...
%C A230324   -6, -9,  22,  104,   -56, -1216,  -608, ...
%C A230324   -3, 31,  82, -160, -1160,   608, 18880, ...
%C A230324 etc.
%C A230324 a(n) is an autosequence: Its inverse binomial transform is the sequence (up to a sign), which means top row and left column in the difference array have the same absolute values.
%C A230324 The main diagonal is the double of the first upper diagonal: A(n,n) = 2*A(n,n+1).
%C A230324 A(n,n+1) = (-1)^n*A005439(n), which also appears as the first upper diagonal of the difference array of A226158(n).
%H A230324 G. C. Greubel, <a href="/A230324/b230324.txt">Table of n, a(n) for n = 0..500</a>
%H A230324 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%F A230324 a(n)/2 + A164555(n)/A027642(n) = 2*A225825(n)/A141056(n).
%e A230324 a(0) =  0 - 2 * (-1) =  2,
%e A230324 a(1) = -1 - 2 * (-1) =  1,
%e A230324 a(2) = -1 - 2 *   0  = -1,
%e A230324 a(3) =  0 - 2 *   1  = -2,
%e A230324 a(4) =  1 - 2 *   0  =  1,
%e A230324 a(5) =  0 - 2 * (-3) =  6.
%p A230324 A226158 := proc(n)
%p A230324     if n = 0 then
%p A230324         0;
%p A230324     else
%p A230324         Zeta(1-n)*2*n*(2^n-1) ;
%p A230324     end if;
%p A230324 end proc:
%p A230324 A230324 := proc(n)
%p A230324     A226158(n)-2*A226158(n+1) ;
%p A230324 end proc: # _R. J. Mathar_, Oct 28 2013
%t A230324 a[0] = 2; a[1] = 1; a[n_] := n EulerE[n-1, 0] - 2 (n+1) EulerE[n, 0];
%t A230324 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Jun 07 2017 *)
%Y A230324 Cf. A050946.
%K A230324 sign
%O A230324 0,1
%A A230324 _Paul Curtz_, Oct 16 2013