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 A181089 Triangle T(n, k) = A060821(n,k) + A060821(n,n-k), read by rows. 2
 2, 2, 2, 2, 0, 2, 8, -12, -12, 8, 28, 0, -96, 0, 28, 32, 120, -160, -160, 120, 32, -56, 0, 240, 0, 240, 0, -56, 128, -1680, -1344, 3360, 3360, -1344, -1680, 128, 1936, 0, -17024, 0, 26880, 0, -17024, 0, 1936, 512, 30240, -9216, -80640, 48384, 48384, -80640, -9216, 30240, 512 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n, k) = coefficients [x^k] of the polynomial HermiteH(n,x) + x^n*HermiteH(n,1/x). T(n, k) = A060821(n,k) + A060821(n,n-k). Sum_{k=0..n} T(n, k) = 2*A062267(n). EXAMPLE Triangle begins as: 2; 2, 2; 2, 0, 2; 8, -12, -12, 8; 28, 0, -96, 0, 28; 32, 120, -160, -160, 120, 32; -56, 0, 240, 0, 240, 0, -56; 128, -1680, -1344, 3360, 3360, -1344, -1680, 128; 1936, 0, -17024, 0, 26880, 0, -17024, 0, 1936; 512, 30240, -9216, -80640, 48384, 48384, -80640, -9216, 30240, 512; MATHEMATICA (* First program *) p[x_, n_] = HermiteH[n, x] + ExpandAll[x^n*HermiteH[n, 1/x]]; Flatten[Table[CoefficientList[p[x, n], x], {n, 0, 15}]] (* edited by G. C. Greubel, Apr 04 2021 *) (* Second program *) A060821[n_, k_]:= If[EvenQ[n-k], (-1)^(Floor[(n-k)/2])*2^k*n!/(k!*(Floor[(n - k)/2]!)), 0]; T[n_, k_]:= A060821[n, k] +A060821[n, n-k]; Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* 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 T(n, k): return A060821(n, k) + A060821(n, n-k) flatten([[T(n, k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Apr 04 2021 CROSSREFS Cf. A060821, A062267. Sequence in context: A097033 A268686 A113306 * A341894 A171932 A358094 Adjacent sequences: A181086 A181087 A181088 * A181090 A181091 A181092 KEYWORD sign,tabl AUTHOR Roger L. Bagula, Oct 02 2010 STATUS approved

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Last modified June 18 08:27 EDT 2024. Contains 373472 sequences. (Running on oeis4.)