A397744 Number of assembly trees for the n-barbell graph.

1, 5, 117, 6489, 658485, 106430625, 25118936325, 8155198067625, 3487089096847125, 1899731241471380625, 1284694587236408473125, 1055971667165040426425625, 1036878703966440780963643125, 1198747700236534020909882170625, 1611760245892952477624798223853125

Offset

1,2

Links

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

Eric Weisstein's World of Mathematics, Assembly Number.

Eric Weisstein's World of Mathematics, Barbell Graph.

Formula

a(n) = Sum_{i=0..n-1} Sum_{j=0..n-1} binomial(i+j,i) * A193229(n-1,i) * A193229(n-1, j).

Prog

(PARI)
T(n, k) = { (2*n-k)!/(2^(n-k)*(n-k)!) } \\ A193229
a(n) = {sum(i=0, n-1, sum(j=0, n-1, T(n-1, i)*T(n-1, j)*binomial(i+j, i) ))}

Crossrefs

Cf. A193229.

Sequence in context: A006221 A265977 A208387 * A144998 A257865 A212040

Adjacent sequences: A397738 A397741 A397743 * A397745 A397746 A397747

Keyword

nonn,new

Author

Andrew Howroyd, Jul 08 2026

Status

approved