A288841 Number of matchings in the n-barbell graph.

2, 5, 20, 116, 776, 6452, 59600, 637520, 7448096, 97038416, 1364378432, 20916787520, 342839381120, 6037591428416, 112827290045696, 2242175347188992, 46994011015447040, 1039493812105176320, 24127862805479576576, 587607347568497570816

Offset

1,1

Comments

Sequence extended to n=1 using formula. - Andrew Howroyd, Jun 19 2017

Links

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

Eric Weisstein's World of Mathematics, Barbell Graph

Eric Weisstein's World of Mathematics, Independent Edge Set

Eric Weisstein's World of Mathematics, Matching

Formula

a(n) = A000085(n)^2 + A000085(n-1)^2. - Andrew Howroyd, Jun 19 2017

Mathematica

Table[(-(1/2))^n (HermiteH[n, -(I/Sqrt[2])]^2 - 2 HermiteH[-1 + n, -(I/Sqrt[2])]^2), {n, 20}]
Table[(-2)^(n - 2) (HypergeometricU[1 - n/2, 3/2, -(1/2)]^2 + 4 HypergeometricU[-(n/2), 1/2, -(1/2)]^2), {n, 20}]
Total /@ (Partition[Range[0, 20]! CoefficientList[Series[Exp[x + x^2/2], {x, 0, 20}], x], 2, 1]^2)

Prog

(PARI)
b(n) = n! * polcoeff( exp( x + x^2 / 2 + x * O(x^n)), n);
a(n) = b(n)^2+b(n-1)^2; \\ Andrew Howroyd, Jun 19 2017

Crossrefs

Cf. A000085.

Sequence in context: A168357 A052850 A000130 * A009599 A112833 A144503

Adjacent sequences: A288838 A288839 A288840 * A288842 A288843 A288844

Keyword

nonn

Author

Eric W. Weisstein, Jun 17 2017

Extensions

a(1)-a(2) inserted by Andrew Howroyd, Jun 19 2017

Status

approved