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 A181088 a(n) = A181089(2*n+1,n)/(n+2). 1
 1, -4, -40, 672, 8064, -253440, -3294720, 153753600, 2091048960, -130025226240, -1820353167360, 141707492720640, 2024392753152000, -189483161695027200, -2747505844577894400, 300609462994993152000, 4408938790593232896000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS What are the constraints on left-right symmetric triangles t(n,m) such that t(2*n,n)/(n+1) are integers? LINKS G. C. Greubel, Table of n, a(n) for n = 0..450 FORMULA a(n) = (A060821(2*n+1, n) + A060821(2*n+1, n+1))/(n+2). - G. C. Greubel, Apr 04 2021 MATHEMATICA (* 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]; a[n_]:= (A060821[2*n+1, n] + A060821[2*n+1, n+1])/(n+2); Table[a[n], {n, 0, 25}] (* G. C. Greubel, Apr 04 2021 *) PROG (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 def a(n): return (A060821(2*n+1, n) + A060821(2*n+1, n+1))/(n+2) [a(n) for n in (0..25)] # G. C. Greubel, Apr 04 2021 CROSSREFS Cf. A060821, A177042, A177043, A181089. Sequence in context: A343446 A205671 A234294 * A005431 A153849 A372232 Adjacent sequences: A181085 A181086 A181087 * A181089 A181090 A181091 KEYWORD sign AUTHOR Roger L. Bagula, Oct 02 2010 STATUS approved

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Last modified June 25 13:13 EDT 2024. Contains 373705 sequences. (Running on oeis4.)