OFFSET
0,6
COMMENTS
Number of cycles in K_n - P_n. - Sean A. Irvine, Jan 17 2017
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
F. C. Holroyd and W. J. G. Wingate, Cycles in the complement of a tree or other graph, Discrete Math., 55 (1985), 267-282.
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Path Complement Graph
FORMULA
a(n) = (1/2)*Sum_{k=3..n} Sum_{i=1..k} Sum_{j=0..k-i} (-1)^(k-i)*(i-1)!*2^j*binomial(n+i-k, i)*binomial(i, j)*binomial(k-i-1, k-i-j). - Andrew Howroyd, Apr 21 2018
a(n) ~ (n-1)! / (2*exp(1)). - Vaclav Kotesovec, Apr 22 2018
MATHEMATICA
Array[(1/2)Sum[Sum[Sum[(-1)^(k - i) (i - 1)!*2^j*Binomial[# + i - k, i] Binomial[i, j] Binomial[k - i - 1, k - i - j], {j, 0, k - i}], {i, k}], {k, 3, #}] &, 28, 0] (* Michael De Vlieger, Apr 21 2018 *)
Table[Sum[(-1)^(k - i) Gamma[i] 2^j Binomial[n + i - k, i] Binomial[i, j] Binomial[k - i - 1, k - i - j], {k, 3, n}, {i, k}, {j, 0, k - i}]/2, {n, 20}] (* Eric W. Weisstein, Apr 23 2018 *)
PROG
(PARI) a(n)={sum(k=3, n, sum(i=1, k, sum(j=0, min(i, k-i), (-1)^(k-i)*(i-1)!*2^j*binomial(n+i-k, i)*binomial(i, j)*binomial(k-i-1, k-i-j))))/2} \\ Andrew Howroyd, Apr 21 2018
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
EXTENSIONS
a(0)-a(3) prepended, a(4) corrected, and more terms from Sean A. Irvine, Jan 17 2017
STATUS
approved