%I A072287
%S A072287 1,2,7,47,155,2027,6597,42835,138875,3599155,11654465,75457289,
%T A072287 244238477,3161900479,10232916665,66231885067,214336798299,
%U A072287 11097918730051,35913975952793,232441522435405,752199270651129
%N A072287 Let f(n, m) = binomial(n - m/2 + 1, n - m + 1) - binomial(n - m/2, n 
               - m + 1) and let s(n) = Sum_{k=0..n} f(n, k); then a(n) = numerator 
               of s(n).
%F A072287 s(0)=1, s(1)=2, s(n+1)=s(n)+s(n-1)+binomial(n-1/2, n) for n>=1.
%e A072287 1,2,7/2,47/8,155/16,2027/128,6597/256,42835/1024,138875/2048,...
%t A072287 f[n_, m_] := Binomial[n - m/2 + 1, n - m + 1] - Binomial[n - m/2, n - 
               m + 1]; s[n_] := Sum[ f[n, k], {k, 0, n}]; Table [Numerator[s[n]], 
               {n, 0, 26}]
%Y A072287 Denominator of s(n+1) = A046161(n).
%Y A072287 Sequence in context: A062632 A116892 A054555 this_sequence A091117 A056854 
               A117141
%Y A072287 Adjacent sequences: A072284 A072285 A072286 this_sequence A072288 A072289 
               A072290
%K A072287 nonn,easy,frac
%O A072287 0,2
%A A072287 Michele Dondi (bik.mido(AT)tiscalinet.it), Jul 11, 2002