A290755 Number of minimal edge covers in the n-crown graph.

1, 0, 1, 5, 49, 759, 16081, 435833, 14517441, 579937319, 27203499361, 1474723875789, 91200920752129, 6365087902895747, 496792437580978449, 43025414912824996889, 4106965602739453756801, 429531453143336097416367, 48964278165034713331278529, 6055596695306076807138311717, 809134978410285605488807023681

Offset: 0

Author

Eric W. Weisstein, Aug 09 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..60
• Eric Weisstein's World of Mathematics, Crown Graph.
• Eric Weisstein's World of Mathematics, Minimal Edge Cover.

Crossrefs

Cf. A210655.

Programs

PARI

\\ by inclusion-exclusion.
B(n,k)={ my(xe=exp(x+O(x*x^n)), ye=exp(y+O(y*y^n))); n!^2*polcoef(polcoef((xe+ye-1)^k*exp(x*ye + y*xe - (x+y+x*y)),n),n)}
a(n) = {sum(k=0, n, binomial(n,k)*B(n-k,k)*(-1)^k)} \\ Andrew Howroyd, May 29 2025

Extensions

a(6)-a(8) from Giovanni Resta, Aug 10 2017

a(1)-a(2) inserted by Eric W. Weisstein, Feb 14 2022

a(0)=1 prepended and a(9) onwards from Andrew Howroyd, May 29 2025