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

0,4

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.

Prog

(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

Crossrefs

Cf. A210655.

Sequence in context: A390059 A390302 A357335 * A062995 A293847 A104600

Adjacent sequences: A290752 A290753 A290754 * A290756 A290757 A290758

Keyword

nonn

Author

Eric W. Weisstein, Aug 09 2017

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

Status

approved