A056457 Palindromes using exactly six different symbols.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 720, 720, 15120, 15120, 191520, 191520, 1905120, 1905120, 16435440, 16435440, 129230640, 129230640, 953029440, 953029440, 6711344640, 6711344640, 45674188560

Offset: 1

Author

Marks R. Nester

Keywords

• nonn
• easy

References

• M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2.]

Links

• Index entries for linear recurrences with constant coefficients, signature (1,20,-20,-155,155,580,-580,-1044,1044,720,-720).

Crossrefs

Cf. A056452, A000920.

Programs

Mathematica

k=6; Table[k! StirlingS2[Ceiling[n/2],k],{n,1,30}]

PARI

a(n) = 6!*stirling((n+1)\2, 6, 2); \\ Altug Alkan, Sep 25 2018

Formula

a(n) = 6! * Stirling2( [(n+1)/2], 6).

G.f.: 720*x^11/((x-1)*(2*x-1)*(2*x+1)*(2*x^2-1)*(3*x^2-1)*(5*x^2-1)*(6*x^2-1)). - Colin Barker, Sep 03 2012

G.f.: k!(x^(2k-1)+x^(2k))/Product_{i=1..k}(1-ix^2), where k=6 is the number of symbols. - Robert A. Russell, Sep 25 2018