cp's OEIS Frontend

A090145 Even-indexed terms of the binomial transform equal 1 and the odd-indexed terms of the second binomial transform equal 1.

%I A090145 #9 May 10 2013 18:10:25
%S A090145 1,-1,2,-7,20,-31,2,-127,1640,-511,-49498,-2047,2706860,-8191,
%T A090145 -199344598,-32767,19391577680,-131071,-2404879413298,-524287,
%U A090145 370371189286100,-2097151,-69348874388943598,-8388607,15514534163573864120,-33554431,-4087072509293056783498
%N A090145 Even-indexed terms of the binomial transform equal 1 and the odd-indexed terms of the second binomial transform equal 1.
%F A090145 E.g.f.: 2*((1 + sinh(x))*exp(x) - sinh(x)) / (exp(x)*(1 + exp(2*x))).
%F A090145 a(2n+1) = 1 - 2^(2n+1);
%F A090145 1 = sum_{k=0..2n} C(2n, k)*a(k);
%F A090145 1 = sum_{k=0..2n-1} 2^(2n-1-k)*C(2n-1, k)*a(k).
%e A090145 a(11) = 1 - 2^11 = -2047.
%e A090145 First binomial  = {1, 0, 1, -3, 1, 15, 1, -273, 1, 7935, 1, -353793,..};
%e A090145 Second binomial = {1, 1, 2, 1, -4, 1, 62, 1, -1384, 1, 50522, 1, -2702764,..}.
%Y A090145 Cf. A090158.
%K A090145 sign
%O A090145 0,3
%A A090145 _Paul D. Hanna_, Nov 22 2003