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

2, 1, -1, -2, 1, 6, -3, -34, 17, 310, -155, -4146, 2073, 76454, -38227, -1859138, 929569, 57641238, -28820619, -2219305810, 1109652905, 103886563462, -51943281731, -5810302084962, 2905151042481, 382659344967926

Offset: 0

Author

Paul Curtz, Oct 16 2013

Keywords

• sign

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).

A(n,n+1) = (-1)^n*A005439(n), which also appears as the first upper diagonal of the difference array of A226158(n).

Examples

			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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• OEIS Wiki, Autosequence

Crossrefs

Cf. A050946.

Programs

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)
    A226158(n)-2*A226158(n+1) ;
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 *)

Formula

a(n)/2 + A164555(n)/A027642(n) = 2*A225825(n)/A141056(n).