|
| |
|
|
A001814
|
|
Coefficient of H_2 when expressing x^{2n} in terms of Hermite polynomials H_m.
(Formerly M4875 N2088)
|
|
7
| |
|
|
1, 12, 180, 3360, 75600, 1995840, 60540480, 2075673600, 79394515200, 3352212864000, 154872234316800, 7771770303897600, 420970891461120000, 24481076457277440000, 1521324036987955200000, 100610229646136770560000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| a(n)=A126804(n)/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 21 2007
|
|
|
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.
H. E. Salzer, Coefficients for expressing the first thirty powers in terms of the Hermite polynomials, Math. Comp., 3 (1948), 167-169.
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
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
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
|
|
|
FORMULA
| E.g.f.: x*(1 + 2x)/(1 - 4x)^(5/2).
a(n) = (2*n)!/(2*(n-1)!).
(n!/2)*binomial(2*n,n)*n or n!/2*A005430 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2006
|
|
|
MAPLE
| with(combinat):for n from 1 to 16 do printf(`%d, `, n!/2*sum(binomial(2*n, n), k=1..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2007
a:=n->sum((count(Permutation(n*2+2), size=n+1)), j=0..n)/2: seq(a(n), n=0..15); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 03 2007
seq(1/2*mul((n+k), k=1..n), n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 21 2007
|
|
|
MATHEMATICA
| Table[(2*n)!/(2*(n-1)!), {n, 1, 20}] (* Vincenzo Librandi, Nov 22 2011 *)
|
|
|
PROG
| (Mupad) combinat::catalan(n)*binomial(n+1, 2)*n! $ n = 1..16; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 15 2007
(MAGMA) [Factorial(2*n)/(2*Factorial(n-1)): n in [1..20]]; // Vincenzo Librandi, Nov 22 2011
|
|
|
CROSSREFS
| a(n) = A048854(n, 1) = A067147(2n, 2).
Cf. A001879.
Cf. A005430.
Sequence in context: A069685 A000515 A051609 * A013924 A145560 A166773
Adjacent sequences: A001811 A001812 A001813 * A001815 A001816 A001817
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms and new description from Christian G. Bower (bowerc(AT)usa.net), Dec 18 2001
|
| |
|
|
