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.

1, 2, 1, 4, 4, 2, 8, 12, 12, 3, 16, 32, 48, 24, 6, 32, 80, 160, 120, 60, 10, 64, 192, 480, 480, 360, 120, 20, 128, 448, 1344, 1680, 1680, 840, 280, 35, 256, 1024, 3584, 5376, 6720, 4480, 2240, 560, 70, 512, 2304, 9216, 16128, 24192

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl

Comments

P(n,k,n) counts palindromes.

Examples

			Triangle begins:
   1;
   2,  1;
   4,  4,  2;
   8, 12, 12,  3;
  16, 32, 48, 24, 6;
  ...
		

Crossrefs

Cf. A001700 (row sums), A051287, A051288, A051290.

Formula

E.g.f.: exp(2*y)*(BesselI(0, 2*x*y)+BesselI(1, 2*x*y)). - Vladeta Jovovic, Dec 15 2004