A001816 - OEIS

A001816

Coefficients of x^n in Hermite polynomial H_{n+4}
(Formerly M4862 N2078)

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

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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