|
|
A270229
|
|
Number of matchings (i.e., Hosoya index) in P_{2} X K_{n}.
|
|
4
|
|
|
1, 2, 7, 32, 193, 1382, 11719, 112604, 1221889, 14639786, 192949639, 2760749048, 42732172993, 709490574158, 12596398359367, 237750425419508, 4757710386662401, 100516614496518866, 2236829315345704711, 52262526676903613264, 1279512810244450887361
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Sequence extended to n=0 using closed form. (binomial transform of A111883)
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (n+1)*a(n-1) + (n-1)^2*a(n-2) - (n-2)*(n-1)^2*a(n-3) + (n-3)*(n-2)*(n-1)*a(n-4).
E.g.f.: exp((2-x)*x/(1-x)) / sqrt(1-x^2).
a(n) ~ exp(1/2 + 2*sqrt(n) - n) * n^n / 2.
(End)
|
|
MATHEMATICA
|
a[n_] := Sum[Binomial[n, k]*Abs[HermiteH[k, I/Sqrt[2]]]^2/2^k, {k, 0, n}];
CoefficientList[Series[E^((2-x)*x/(1-x)) / Sqrt[1-x^2], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2017 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|