A351589 Number of minimal edge covers in the n-cocktail party graph.
0, 2, 74, 2228, 100494, 6014932, 453143662, 41921209920, 4639656895118, 603202689990836, 90714189165482310, 15583340701180474312, 3025677781064563172326, 658038493760685537784572, 159065982382639942877853134, 42449055613405195868802686816
Offset: 1
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..100
- Eric Weisstein's World of Mathematics, Cocktail Party Graph
- Eric Weisstein's World of Mathematics, Minimal Edge Cover
Programs
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PARI
a(n)={my(x=x+O(x^(2*n+1)), p=exp(-x - x^2/2 + x*exp(x)), q=2*exp(x) - 1); sum(k=0, n, (-1)^(n-k)*binomial(n,k)*(2*k)!*polcoef(q^(n-k)*p, 2*k))} \\ Andrew Howroyd, Feb 21 2022
Formula
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * (2*k)! * [x^(2*k)] B(n-k,x), where B(k,x) = (2*exp(x) - 1)^k * exp(-x - x^2/2 + x*exp(x)). - Andrew Howroyd, Feb 21 2022
Extensions
Terms a(5) and beyond from Andrew Howroyd, Feb 21 2022