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

0,2

Comments

P(n,k,n) counts palindromes.

Links

Table of n, a(n) for n=0..49.

Formula

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

Example

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.

Sequence in context: A247248 A192017 A180566 * A134308 A090802 A379200

Adjacent sequences: A051286 A051287 A051288 * A051290 A051291 A051292

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved