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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
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].
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
Sequence in context: A121032 A188251 A093334 * A354697 A133386 A305624
KEYWORD
nonn,easy
AUTHOR
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.)