cp's OEIS Frontend

A051289 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.

%I A051289 #20 Aug 13 2024 04:59:46
%S A051289 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 A051289 480,360,120,20,128,448,1344,1680,1680,840,280,35,256,1024,3584,5376,
%U A051289 6720,4480,2240,560,70,512,2304,9216,16128,24192
%N A051289 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 A051289 P(n,k,n) counts palindromes.
%F A051289 E.g.f.: exp(2*y)*(BesselI(0, 2*x*y)+BesselI(1, 2*x*y)). - _Vladeta Jovovic_, Dec 15 2004
%e A051289 Triangle begins:
%e A051289    1;
%e A051289    2,  1;
%e A051289    4,  4,  2;
%e A051289    8, 12, 12,  3;
%e A051289   16, 32, 48, 24, 6;
%e A051289   ...
%Y A051289 Cf. A001700 (row sums), A051287, A051288, A051290.
%K A051289 nonn,tabl
%O A051289 0,2
%A A051289 _Clark Kimberling_