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 A054374 Discriminant of Hermite polynomials. 3
 1, 32, 55296, 7247757312, 92771293593600000, 141830962344853556428800000, 30619440571316366848044102687129600000, 1077325790213073725701226681195621188514296627200000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A054374 gives the discriminants of the Hermite polynomials in the conventional (physicists') normalization, and A002109 gives the discriminants of the Hermite polynomials in the (in my opinion more natural) probabilists' normalization. See refs Wikipedia and Szego eq. (6.71.7). - Alan Sokal, Mar 02 2012 REFERENCES G. Szego, Orthogonal Polynomials, American Mathematical Society, 1981 edition, 432 Pages. LINKS Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257.  Mathematical Reviews, MR2312537.  Zentralblatt MATH, Zbl 1133.11012. Eric Weisstein's World of Mathematics, Hermite Polynomial. Wikipedia, Hermite polynomials FORMULA a(n) = 2^(3*n*(n-1)/2) * Product_{k=1..n} k^k. MATHEMATICA Table[2^(3n(n-1)/2)Product[k^k, {k, 1, n}], {n, 1, 8}] (* Indranil Ghosh, Feb 24 2017 *) PROG (PARI) for(n=1, 8, print1(2^(3*n*(n-1)/2)*prod(j=1, n, j^j), ", ")) \\ G. C. Greubel, Jun 10 2018 (MAGMA) [Round(2^(3*n*(n-1)/2)*(&*[j^j: j in [1..n]])): n in [1..8]]; // G. C. Greubel, Jun 10 2018 CROSSREFS Cf. A002109. Sequence in context: A285389 A159396 A221086 * A221138 A017009 A176030 Adjacent sequences:  A054371 A054372 A054373 * A054375 A054376 A054377 KEYWORD nonn AUTHOR STATUS approved

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Last modified February 24 07:19 EST 2020. Contains 332199 sequences. (Running on oeis4.)