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

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