The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A296190 Numerators of Harary index for the n-permutation star graph. 1
 0, 1, 10, 123, 2202, 59040, 2287680, 121394000, 92649740400, 105538103163360, 1034297134668000, 134399089883282400, 27076064087538702720, 5451799851068349018240, 19300076847195336557164800, 4599598343095846092562560000, 1682634821690958905899793664000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The permutation star graph of order n is a vertex transitive graph with n! vertices and degree n-1. The graph can be constructed as the Cayley graph of the permutations of 1..n with the n-1 generators (1 2), (1 3)..(1 n) where (1 k) is the transposition of 1 and k. The number of nodes at distance k from a specified node is given by A007799(n,k). - Andrew Howroyd, Dec 09 2017 LINKS Eric Weisstein's World of Mathematics, Harary Index Eric Weisstein's World of Mathematics, Permutation Star Graph FORMULA a(n)/A296057(n) = (n!/2) * Sum_{k=1..floor(3*(n-1)/2)} A007799(n, k)/k. - Andrew Howroyd, Dec 09 2017 MATHEMATICA A007799[n_, i_] := Sum[Binomial[n - 1, k] Binomial[n - 1 - k, t] StirlingS1[k + 1, i - k + 1 - 2 t] (-1)^(i + 2 - t), {k, 0, Min[n - 1, i + 1]}, {t, Max[0, Ceiling[(i - 2 k)/2]], Min[n - 1 - k, Floor[(i + 1 - k)/2]]}]; Table[n! Sum[A007799[n, k]/k, {k, Floor[3 (n - 1)/2]}]/2, {n, 20}] // Numerator (* Eric W. Weisstein, Dec 09 2017 *) CROSSREFS Cf. A296057 (denominators), A007799, A284039. Sequence in context: A233084 A081784 A239760 * A263552 A259839 A005174 Adjacent sequences:  A296187 A296188 A296189 * A296191 A296192 A296193 KEYWORD nonn,frac AUTHOR Eric W. Weisstein, Dec 07 2017 EXTENSIONS a(9)-a(17) from Andrew Howroyd, Dec 09 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)