A243868 0 followed by -(n+1)*A226158(n).

0, 0, 2, 3, 0, -5, 0, 21, 0, -153, 0, 1705, 0, -26949, 0, 573405, 0, -15802673, 0, 547591761, 0, -23302711005, 0, 1194695479813, 0, -72628776062025, 0, 5165901157067001, 0, -425013158488292213, 0

Offset

0,3

Comments

An autosequence is a sequence which has its inverse binomial transform equal to the signed sequence. If the main diagonal is A000004=0's it is of the first kind. It is of the second kind if the main diagonal is the upper diagonal multiplied by 2.

Starting from the autosequence of second kind A198631(n)/A006519(n+1),the fractional Euler numbers,we build a family of alternated sequences of second and first kind. A row is 0 followed by n+1 times the preceding one.

1, 1/2, 0, -1/4, 0, 1/2, 0, -17/8, 0, 31/2,...

0, 1, 1, 0, -1, 0, 3, 0, -17, 0, 155,... = -A226158(n)

0, 0, 2, 3, 0, -5, 0, 21, 0, -153, 0, 1705,... = a(n).

a(n) is an autosequence of the second kind. Its difference table is:

0, 0, 2, 3, 0, -5, 0, 21, 0, -153,...

0, 2, 1, -3, -5, 5, 21, -21,...

2, -1, -4, -2, 10, 16, -42,...

-3, -3, 2, 12, 6, -58,..

0, 5, 10, -6, -64,...

5, 5, -16, -58,...

0, -21, -42,...

-21, -21,...

0,... .

a(n) is a post Genocchi sequence.

Links

Table of n, a(n) for n=0..30.

Formula

The fourth column of the second triangle of A133135(n) (see also A140218) is

1, -5/2, 5/2, 0, 0, -21/2, 21/2,... = b(n).

c(n) = 0, 0, 0, 0, followed by 2*(-1)^n*b(n) = 0, 0, 0, 0, 2, 5, 5, 0, 0, 21, 21, -132, -132,... . Autosequence.

a(n) = c(n+2) -c(n+1).

Example

a(0)=0, a(1)=1*0=0, a(2)=2*1=2, a(3)=3*1=3, a(4)=4*0=0, a(5)=5*(-1)=-5.

Mathematica

a[0] = a[1] = 0; a[2] = 2; a[n_] := -n*(n-1)*EulerE[n-2, 0]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 17 2014 *)

Crossrefs

Cf. A102055, A230011, A229054.

Sequence in context: A064502 A082809 A070245 * A066398 A138197 A140664

Adjacent sequences: A243865 A243866 A243867 * A243869 A243870 A243871

Keyword

sign,frac,tabl

Author

Paul Curtz, Jun 13 2014

Extensions

More terms from Jean-François Alcover, Jun 17 2014

Status

approved