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A288841
Number of matchings in the n-barbell graph.
3
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
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 17 2017
EXTENSIONS
a(1)-a(2) inserted by Andrew Howroyd, Jun 19 2017
STATUS
approved