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A056457
Palindromes using exactly six different symbols.
6
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
1,11
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).
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
MATHEMATICA
k=6; Table[k! StirlingS2[Ceiling[n/2], k], {n, 1, 30}]
PROG
(PARI) a(n) = 6!*stirling((n+1)\2, 6, 2); \\ Altug Alkan, Sep 25 2018
CROSSREFS
Sequence in context: A267026 A145226 A056467 * A068351 A067892 A337036
KEYWORD
nonn,easy
STATUS
approved