A292062 Wiener index of the n-transposition graph.

0, 1, 21, 552, 19560, 920160, 55974240, 4293596160, 406306575360, 46556342784000, 6357567896064000, 1020650937901056000, 190386526063878144000, 40844355820490686464000, 9987985777548364185600000, 2762125829379285162393600000, 857790151281459139077734400000

Offset: 1

Author

Eric W. Weisstein, Sep 08 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50
• Eric Weisstein's World of Mathematics, Transposition Graph
• Eric Weisstein's World of Mathematics, Wiener Index

Crossrefs

Cf. A067318, A296194.

Programs

Mathematica

Table[n! (n n! + (-1)^n StirlingS1[n + 1, 2])/2, {n, 20}]

PARI

a(n) = n! * (n*n! - abs(stirling(n+1, 2, 1))) / 2; \\ Andrew Howroyd, Sep 08 2017

Formula

From Andrew Howroyd, Sep 08 2017: (Start)

a(n) = n! * A067318(n) / 2.

a(n) = n! * (n*n! - abs(Stirling1(n+1, 2))) / 2.

(End)

a(n) = (n!/2) * Sum_{k=1..n-1} abs(Stirling1(n, n-k))*k. - Andrew Howroyd, Dec 09 2017

Extensions

Terms a(9) and beyond from Andrew Howroyd, Sep 08 2017