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A270229
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Number of matchings in the 2 X n rook graph P_2 X K_n.
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4
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1, 2, 7, 32, 193, 1382, 11719, 112604, 1221889, 14639786, 192949639, 2760749048, 42732172993, 709490574158, 12596398359367, 237750425419508, 4757710386662401, 100516614496518866, 2236829315345704711, 52262526676903613264, 1279512810244450887361
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OFFSET
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0,2
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COMMENTS
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Sequence extended to n=0 using closed form. (binomial transform of A111883)
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LINKS
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FORMULA
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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)
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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