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A217714 Modified Euler numbers.

%I A217714 #31 Jan 24 2020 03:31:18
%S A217714 1,0,-2,-3,4,15,-62,-273,1384,7935,-50522,-353793,2702764,22368255,
%T A217714 -199360982,-1903757313,19391512144,209865342975,-2404879675442,
%U A217714 -29088885112833,370371188237524,4951498053124095,-69348874393137902,-1015423886506852353,15514534163557086904,246921480190207983615,-4087072509293123892362
%N A217714 Modified Euler numbers.
%C A217714 a(n) and differences are:
%C A217714     1,   0,  -2,  -3,   4,  15, -62;
%C A217714    -1,  -2,  -1,   7,  11, -77;
%C A217714    -1,   1,   8,   4, -88;
%C A217714     2,   7,  -4, -92;
%C A217714     5, -11, -88;
%C A217714   -16, -77;
%C A217714   -61;
%C A217714 (See the array in A163982(n) and the comments/examples in A090158 and A090145.)
%C A217714 The absolute values of the first column are A000111(n).
%C A217714 The first column can be found via the Akiyama-Tanigawa algorithm. See the chapter on the Seidel triangle in Wikipedia's Bernoulli Number.
%H A217714 Wikipedia, <a href="http://en.wikipedia.org/wiki/Bernoulli_number#An_algorithmic_view:_the_Seidel_triangle">Bernoulli Number, Seidel triangle</a>
%F A217714 a(n) = -A163982(n) - 1.
%F A217714 a(n) = Sum_{k=0..n} A109449(n,k)*floor((n-k+1)/2). - _Philippe Deléham_, Oct 27 2013
%F A217714 E.g.f.: 1/cosh(x) + tanh(x) + 1 - exp(x). - _Sergei N. Gladkovskii_, Nov 10 2014
%e A217714 a(0) =   1;
%e A217714 a(1) =   1 -   1 = 0;
%e A217714 a(2) =  -1 -   2 +   1 = -2;
%e A217714 a(3) =   2 -   3 -   3 +   1 = -3;
%e A217714 a(4) =   5 +   8 -   6 -   4 +  1 = 4;
%e A217714 a(5) = -16 +  25 +  20 -  10 -  5 +  1 = 15;
%e A217714 a(6) = -61 -  96 +  75 +  40 - 15 -  6 + 1 = -62;
%e A217714 a(7) = 272 - 427 - 336 + 175 + 70 - 21 - 7 + 1 = -273; - _Philippe Deléham_, Oct 27 2013
%e A217714 G.f. = 1 - 2*x^2 - 3*x^3 + 4*x^4 + 15*x^5 - 62*x^6 - 273*x^7 + ...
%t A217714 a[n_] := 2^n* EulerE[n, 1] + EulerE[n] - 1; Table[a[n], {n, 0, 26}] (* _Jean-François Alcover_, Mar 21 2013 *)
%Y A217714 Cf. A000111, A163982.
%K A217714 sign
%O A217714 0,3
%A A217714 _Paul Curtz_, Mar 21 2013
%E A217714 More terms from _Jean-François Alcover_, Mar 21 2013