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%I #12 Jan 22 2020 03:33:07
%S 1,2,7,23,79,272,943,3278,11419,39830,139057,485795,1697905,5936348,
%T 20760271,72615143,254028355,888758030,3109714117,10881403229,
%U 38077702909,133251869648,466325356273,1631981113112,5711490384901
%N A Motzkin transform of Jacobsthal numbers.
%C Binomial transform of A100098.
%C Inverse binomial transform of A007854. The Hankel transform of this sequence is 3^n (see A000244). - _Philippe Deléham_, Nov 25 2007
%F a(n) = Sum_{k=0..n} A026300(n, k)*(2^(k+1) + (-1)^k)/3, where A026300 is the Motzkin triangle; a(n) = Sum_{k=0..n} ((k+1)/(n+1))*Sum_{j=0..n+1} C(n+1, j)*C(j, 2j-n+k)*(2^(k+1) + (-1)^k)/3.
%F a(n) = Sum_{k=0..n} A089942(n,k)*2^k = Sum_{k=0..n} A071947(n,k)*2^(n-k). - _Philippe Deléham_, Mar 31 2007
%Y Cf. A000244, A007854, A026300, A089942, A100098.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jan 11 2006
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