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A090145 Even-indexed terms of the binomial transform equal 1 and the odd-indexed terms of the second binomial transform equal 1. 3

%I #9 May 10 2013 18:10:25

%S 1,-1,2,-7,20,-31,2,-127,1640,-511,-49498,-2047,2706860,-8191,

%T -199344598,-32767,19391577680,-131071,-2404879413298,-524287,

%U 370371189286100,-2097151,-69348874388943598,-8388607,15514534163573864120,-33554431,-4087072509293056783498

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

%F E.g.f.: 2*((1 + sinh(x))*exp(x) - sinh(x)) / (exp(x)*(1 + exp(2*x))).

%F a(2n+1) = 1 - 2^(2n+1);

%F 1 = sum_{k=0..2n} C(2n, k)*a(k);

%F 1 = sum_{k=0..2n-1} 2^(2n-1-k)*C(2n-1, k)*a(k).

%e a(11) = 1 - 2^11 = -2047.

%e First binomial = {1, 0, 1, -3, 1, 15, 1, -273, 1, 7935, 1, -353793,..};

%e Second binomial = {1, 1, 2, 1, -4, 1, 62, 1, -1384, 1, 50522, 1, -2702764,..}.

%Y Cf. A090158.

%K sign

%O 0,3

%A _Paul D. Hanna_, Nov 22 2003

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)