|
|
A217714
|
|
Modified Euler numbers.
|
|
1
|
|
|
1, 0, -2, -3, 4, 15, -62, -273, 1384, 7935, -50522, -353793, 2702764, 22368255, -199360982, -1903757313, 19391512144, 209865342975, -2404879675442, -29088885112833, 370371188237524, 4951498053124095, -69348874393137902, -1015423886506852353, 15514534163557086904, 246921480190207983615, -4087072509293123892362
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
a(n) and differences are:
1, 0, -2, -3, 4, 15, -62;
-1, -2, -1, 7, 11, -77;
-1, 1, 8, 4, -88;
2, 7, -4, -92;
5, -11, -88;
-16, -77;
-61;
The absolute values of the first column are A000111(n).
The first column can be found via the Akiyama-Tanigawa algorithm. See the chapter on the Seidel triangle in Wikipedia's Bernoulli Number.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(0) = 1;
a(1) = 1 - 1 = 0;
a(2) = -1 - 2 + 1 = -2;
a(3) = 2 - 3 - 3 + 1 = -3;
a(4) = 5 + 8 - 6 - 4 + 1 = 4;
a(5) = -16 + 25 + 20 - 10 - 5 + 1 = 15;
a(6) = -61 - 96 + 75 + 40 - 15 - 6 + 1 = -62;
a(7) = 272 - 427 - 336 + 175 + 70 - 21 - 7 + 1 = -273; - Philippe Deléham, Oct 27 2013
G.f. = 1 - 2*x^2 - 3*x^3 + 4*x^4 + 15*x^5 - 62*x^6 - 273*x^7 + ...
|
|
MATHEMATICA
|
a[n_] := 2^n* EulerE[n, 1] + EulerE[n] - 1; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Mar 21 2013 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|