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A300847
a(n) = 12*binomial(n, 5).
0
0, 0, 0, 0, 0, 12, 72, 252, 672, 1512, 3024, 5544, 9504, 15444, 24024, 36036, 52416, 74256, 102816, 139536, 186048, 244188, 316008, 403788, 510048, 637560, 789360, 968760, 1179360, 1425060, 1710072, 2038932, 2416512, 2848032, 3339072, 3895584, 4523904, 5230764
OFFSET
0,6
COMMENTS
Also the number of 5-cycles in the complete graph K_n for n >= 1.
LINKS
F. Harary, B. Manvel, On the number of cycles in a graph, Matemat. casop. 21 (1971) 55-63, Theorem 2 for 5-cycles in complete graph.
Eric Weisstein's World of Mathematics, Complete Graph
Eric Weisstein's World of Mathematics, Graph Cycle
FORMULA
G.f.: 12*x^5/(x - 1)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) + 6*a(n-4) - a(n-5).
a(n) = A052787(n)/10 = 12*A000389(n).
a(n) = (n - 4)*(n - 3)*(n - 2)*(n - 1)*n/10.
MATHEMATICA
Table[12 Binomial[n, 5], {n, 0, 20}]
12 Binomial[Range[0, 20], 5]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 0, 0, 12, 72}, {0, 20}]
CoefficientList[Series[12 x^5/(x - 1)^6, {x, 0, 20}], x]
PROG
(PARI) a(n) = 12*binomial(n, 5); \\ Altug Alkan, Mar 13 2018
CROSSREFS
Sequence in context: A374374 A188660 A047928 * A235870 A008533 A010024
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 13 2018
STATUS
approved