A122932 a(n) = A000085(n) - A000079(n-1).

0, 0, 0, 2, 10, 44, 168, 636, 2364, 8984, 34672, 138104, 564408, 2382288, 10333152, 46173968, 211733776, 997182752, 4809439296, 23758139808, 119951644320, 618882541760, 3257839688320, 17492182188992, 95680426983360

Offset: 1

Author

Alford Arnold, Sep 22 2006

Keywords

• easy
• nonn

Comments

Also sums values in A117506 but not in A007318.

Examples

			Row five of A117506 is 1 5 9 5 10 16 5 10 9 5 1.
Row five of A007318 is 1 5 10 10 5 1.
So included values are 9 5 16 5 9;
therefore a(5) = 44 = 76 - 32.
		

Crossrefs

Cf. A000079, A000085, A059797, A067924, A117506.

Programs

Mathematica

Table[Sum[(2k)!/k!/2^k Binomial[n, 2k], {k, 0, n/2}] - 2^(n - 1) // FullSimplify, {n, 26}] (* Robert G. Wilson v, Sep 27 2006 *)  (* or *)
Table[HypergeometricU[ -(n/2), 1/2, -(1/2)]/(-(1/2))^(-(-n/2)) - 2^(n - 1), {n, 26}] (* Robert G. Wilson v, Sep 27 2006 *)  (* or *)
(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Table[NumberOfTableaux[M[Star[n+1]]] - 2^(n - 1), {n, 26}] (* Robert G. Wilson v, Sep 27 2006 *)

Formula

a(n) = A000085(n) - A000079(n) for n>0.

Extensions

More terms from Robert G. Wilson v, Sep 27 2006