A178113 - OEIS

%I #12 Feb 09 2025 02:40:48

%S 1,2,2,4,5,10,13,26,35,70,96,192,267,534,750,1500,2123,4246,6046,

%T 12092,17303,34606,49721,99442,143365,286730,414584,829168,1201917,

%U 2403834,3492117,6984234,10165779,20331558,29643870,59287740,86574831,173149662

%N Transform of C(n+1,floor((n+1)/2)) by A178112.

%C Hankel transform is A178115.

%F a(n) = Sum_{k=0..n} C(floor(n/2),floor(k/2))*((1+(-1)^(n-k))/2)*C(k+1,floor((k+1)/2)). [The formula seems to generate A026392, not these terms. - _R. J. Mathar_, Feb 10 2015]

%F Conjecture: a(2*n) = A005773(n+1), a(2*n+1) = 2*a(2*n). - _Jason Yuen_, Feb 09 2025

%Y Cf. A178112, A178115, A005773.

%K easy,nonn

%O 0,2

%A _Paul Barry_, May 20 2010