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
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 17 2017
EXTENSIONS
a(1)-a(2) inserted by Andrew Howroyd, Jun 19 2017
STATUS
approved