A351588 Number of minimal edge covers in the n-path complement graph.

0, 0, 0, 1, 7, 34, 174, 1079, 7055, 48796, 366180, 2928387, 24726556, 220572828, 2071469527, 20393131971, 209934610376, 2254860549906, 25210893460938, 292826210789807, 3527105947667676, 43985152403166462, 567048383126842506, 7546842245268945427, 103560659196050026908

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Minimal Edge Cover.

Eric Weisstein's World of Mathematics, Path Complement Graph.

Formula

a(n) = Sum_{i=0..floor(n/2)} Sum{j=0..floor((n-2*i)/3)} (-1)^i * binomial(i+j,i) * binomial(n-i-2*j,i+j) * (n-2*i-3*j)! * [x^(n-2*i-3*j)] ((2*exp(x)-1)^i * exp(x)^j * exp(-x - x^2/2 + x*exp(x))). - Andrew Howroyd, Jun 14 2025

Prog

(PARI) a(n)={sum(i=0, n\2, sum(j=0, (n-2*i)\3, my(r=n-2*i-3*j, g=exp(x + O(x*x^r))); (-1)^i*binomial(i+j, i)*binomial(n-i-2*j, i+j)*(r)!*polcoef((2*g-1)^i*exp(j*x -x - x^2/2 + x*g), r)))} \\ Andrew Howroyd, Jun 14 2025

Crossrefs

Cf. A302719, A302749, A351587.

Sequence in context: A209890 A027209 A209807 * A080048 A177140 A372411

Adjacent sequences: A351585 A351586 A351587 * A351589 A351590 A351591

Keyword

nonn

Author

Eric W. Weisstein, Feb 14 2022

Extensions

a(9)-a(12) from Andrew Howroyd, Feb 21 2022

a(13) onwards from Andrew Howroyd, Jun 14 2025

Status

approved