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 A001816 Coefficients of x^n in Hermite polynomial H_{n+4} (Formerly M4862 N2078) 2
 12, 120, 720, 3360, 13440, 48384, 161280, 506880, 1520640, 4392960, 12300288, 33546240, 89456640, 233963520, 601620480, 1524105216, 3810263040, 9413591040, 23011000320, 55710842880, 133706022912, 318347673600, 752458137600, 1766640844800, 4122161971200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 801. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 0..500 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. Index entries for sequences related to Hermite polynomials. Index entries for linear recurrences with constant coefficients, signature (10, -40, 80, -80, 32). FORMULA a(n) = 12*A003472(n+4) = A060821(4+n, n). G.f.: 12 ( 1 - 2 x )^(-5). From Amiram Eldar, May 06 2022: (Start) Sum_{n>=0} 1/a(n) = 5/9 - 2*log(2)/3. Sum_{n>=0} (-1)^n/a(n) = 18*log(3/2) - 65/9. (End) MATHEMATICA Table[Coefficient[HermiteH[n + 4, x], x, n], {n, 0, 25}] (* T. D. Noe, Aug 10 2012 *) PROG (PARI) a(n) = polcoeff(polhermite(n+4), n); \\ Michel Marcus, May 06 2022 CROSSREFS Cf. A003472, A060821. Sequence in context: A121032 A188251 A093334 * A354697 A133386 A305624 Adjacent sequences: A001813 A001814 A001815 * A001817 A001818 A001819 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Simon Plouffe EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Jan 29 2001 STATUS approved

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Last modified February 22 16:01 EST 2024. Contains 370256 sequences. (Running on oeis4.)