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A181088
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a(n) = A181089(2*n+1,n)/(n+2).
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1
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1, -4, -40, 672, 8064, -253440, -3294720, 153753600, 2091048960, -130025226240, -1820353167360, 141707492720640, 2024392753152000, -189483161695027200, -2747505844577894400, 300609462994993152000, 4408938790593232896000
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OFFSET
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0,2
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COMMENTS
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What are the constraints on left-right symmetric triangles t(n,m) such that t(2*n,n)/(n+1) are integers?
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LINKS
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FORMULA
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MATHEMATICA
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(* First program *)
p[x_, n_] = HermiteH[n, x] + ExpandAll[x^n*HermiteH[n, 1/x]];
b:= Table[CoefficientList[p[x, n], x], {n, 0, 50}];
Table[b[[2*n+2, n+1]]/(n+2), {n, 0, 20}]
(* Second program *)
A060821[n_, k_]:= If[EvenQ[n-k], (-1)^(Floor[(n-k)/2])*2^k*n!/(k!*(Floor[(n - k)/2]!)), 0];
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PROG
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(Sage)
def A060821(n, k): return (-1)^((n-k)//2)*2^k*factorial(n)/(factorial(k)*factorial( (n-k)//2)) if (n-k)%2==0 else 0
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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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