OFFSET
0,1
COMMENTS
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:
2, 1, -1, -2, 1, 6, -3, ...
-1, -2, -1, 3, 5, -9, -31, ...
-1, 1, 4, 2, -14, -22, 82, ...
2, 3, -2, -16, -8, 104, 160, ...
1, -5, -14, 8, 112, 56, -1160, ...
-6, -9, 22, 104, -56, -1216, -608, ...
-3, 31, 82, -160, -1160, 608, 18880, ...
etc.
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.
The main diagonal is the double of the first upper diagonal: A(n,n) = 2*A(n,n+1).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
OEIS Wiki, Autosequence
EXAMPLE
a(0) = 0 - 2 * (-1) = 2,
a(1) = -1 - 2 * (-1) = 1,
a(2) = -1 - 2 * 0 = -1,
a(3) = 0 - 2 * 1 = -2,
a(4) = 1 - 2 * 0 = 1,
a(5) = 0 - 2 * (-3) = 6.
MAPLE
A226158 := proc(n)
if n = 0 then
0;
else
Zeta(1-n)*2*n*(2^n-1) ;
end if;
end proc:
A230324 := proc(n)
end proc: # R. J. Mathar, Oct 28 2013
MATHEMATICA
a[0] = 2; a[1] = 1; a[n_] := n EulerE[n-1, 0] - 2 (n+1) EulerE[n, 0];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jun 07 2017 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Curtz, Oct 16 2013
STATUS
approved