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A357266 Number of n-node tournaments that have exactly five circular triads. 2
24, 3648, 90384, 1304576, 19958400, 311592960, 5054353920, 85709352960, 1523221539840, 28387834675200, 554575551129600, 11345938174771200, 242796629621145600, 5427273747293798400, 126546947417899008000 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

LINKS

Table of n, a(n) for n=5..19.

J. B. Kadane, Some equivalence classes in paired comparisons, The Annals of Mathematical Statistics, 37 (1966), 488-494.

FORMULA

Kadane proves that a(n) = n!*((1/5)*(n-4)+(14/3)*(n-5)+8*(n-6)I(n>5)+(7/9)*(n-6)*(n-7)I(n>5)+(10/3)*(n-7)*(n-8)I(n>6)+(5/18)*(n-8)*(n-9)*(n-10)I(n>7)+(1/162)*(n-9)*(n-10)*(n-11)*(n-12)I(n>8)+(1/29160)*(n-10)*(n-11)*(n-12)*(n-13)*(n-14)I(n>9)), where I(p) is the indicator function: 1 if p is true and 0 otherwise.

E.g.f.: (5*x^10-180*x^9+2205*x^8-12150*x^7+34155*x^6-51840*x^5+38313*x^4-3942*x^3-11502*x^2+4698*x+243)*x^5/(5*3^5*(1-x)^6).

CROSSREFS

Cf. A357242, A357248, A357257.

Sequence in context: A275637 A223123 A278651 * A166768 A326120 A159399

Adjacent sequences: A357263 A357264 A357265 * A357267 A357268 A357269

KEYWORD

nonn,easy

AUTHOR

Ian R Harris, Ryan P. A. McShane, Sep 22 2022

STATUS

approved

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Last modified November 30 19:00 EST 2022. Contains 358453 sequences. (Running on oeis4.)