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%I #20 Aug 13 2024 04:59:46
%S 1,2,1,4,4,2,8,12,12,3,16,32,48,24,6,32,80,160,120,60,10,64,192,480,
%T 480,360,120,20,128,448,1344,1680,1680,840,280,35,256,1024,3584,5376,
%U 6720,4480,2240,560,70,512,2304,9216,16128,24192
%N Triangular array T read by rows: T(n,k)=P(2n+1,n,2k+1), where P(n,k,c)=number of vectors (x(1),x(2,),...,x(n)) of k 1's and n-k 0's such that x(i)=x(n+1-i) for exactly c values of i.
%C P(n,k,n) counts palindromes.
%F E.g.f.: exp(2*y)*(BesselI(0, 2*x*y)+BesselI(1, 2*x*y)). - _Vladeta Jovovic_, Dec 15 2004
%e Triangle begins:
%e 1;
%e 2, 1;
%e 4, 4, 2;
%e 8, 12, 12, 3;
%e 16, 32, 48, 24, 6;
%e ...
%Y Cf. A001700 (row sums), A051287, A051288, A051290.
%K nonn,tabl
%O 0,2
%A _Clark Kimberling_