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A144141
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a(n) = Hermite(n,2).
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3
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1, 4, 14, 40, 76, -16, -824, -3104, -880, 46144, 200416, -121216, -4894016, -16666880, 60576896, 708980224, 1018614016, -18612911104, -109084520960, 233726715904, 5080118660096, 10971406004224, -169479359707136, -1160659303014400, 3153413334470656
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: exp(4*x - x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*4^(n-2*k)/(k!*(n-2*k)!). (End)
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MATHEMATICA
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lst={}; Do[AppendTo[lst, HermiteH[n, 2]], {n, 0, 7^2}]; lst
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PROG
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(PARI) for(n=0, 50, print1(polhermite(n, 2), ", " )) \\ G. C. Greubel, Jul 10 2018
(Magma) [(&+[(-1)^k*Factorial(n)*(4)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]]): n in [0..30]]; // G. C. Greubel, Jul 10 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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