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 A143507 Triangle of coefficients of x^n*H_n(x + 1/x), where H_n(x) is the Hermite polynomial of order n. 2
 1, 2, 0, 2, 4, 0, 6, 0, 4, 8, 0, 12, 0, 12, 0, 8, 16, 0, 16, 0, 12, 0, 16, 0, 16, 32, 0, 0, 0, -40, 0, -40, 0, 0, 0, 32, 64, 0, -96, 0, -240, 0, -280, 0, -240, 0, -96, 0, 64, 128, 0, -448, 0, -672, 0, -560, 0, -560, 0, -672, 0, -448, 0, 128, 256, 0, -1536, 0, -896, 0, 896, 0, 1680, 0, 896, 0, -896, 0, -1536, 0, 256, 512, 0, -4608, 0, 512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums yield A144141. LINKS Table of n, a(n) for n=0..85. Wikipedia, Hermite polynomials FORMULA E.g.f.: exp(2*(1 + x^2)*y - x^2*y^2). - Franck Maminirina Ramaharo, Oct 25 2018 EXAMPLE Triangle begins: 1; 2, 0, 2; 4, 0, 6, 0, 4; 8, 0, 12, 0, 12, 0, 8; 16, 0, 16, 0, 12, 0, 16, 0, 16; 32, 0, 0, 0, -40, 0, -40, 0, 0, 0, 32; 64, 0, -96, 0, -240, 0, -280, 0, -240, 0, -96, 0, 64; 128, 0, -448, 0, -672, 0, -560, 0, -560, 0, -672, 0, -448, 0, 128; ... reformatted. - Franck Maminirina Ramaharo, Oct 25 2018 MATHEMATICA Table[CoefficientList[FullSimplify[x^n*HermiteH[n, x + 1/x]], x], {n, 0, 10}]//Flatten PROG (PARI) row(n) = Vec(x^n*subst(polhermite(n, x), x, x+1/x)); for (n=0, 10, print(row(n))); \\ Michel Marcus, Oct 27 2018 CROSSREFS Cf. A060821. Cf. A143505, A143506. Sequence in context: A137312 A137320 A263399 * A172040 A317327 A120557 Adjacent sequences: A143504 A143505 A143506 * A143508 A143509 A143510 KEYWORD sign,tabf AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 25 2008 EXTENSIONS Edited, new name and offset corrected by Franck Maminirina Ramaharo, Oct 25 2018 STATUS approved

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Last modified May 23 07:28 EDT 2024. Contains 372760 sequences. (Running on oeis4.)