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A000321
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H_n(-1/2), where H_n(x) is Hermite polynomial of degree n.
(Formerly M3732 N1526)
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3
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1, -1, -1, 5, 1, -41, 31, 461, -895, -6481, 22591, 107029, -604031, -1964665, 17669471, 37341149, -567425279, -627491489, 19919950975, 2669742629, -759627879679, 652838174519, 31251532771999, -59976412450835, -1377594095061119, 4256461892701199, 64623242860354751
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| Koichi, Yamamoto, An asymptotic series for the number of three-line Latin rectangles, J. Math. Soc. Japan 1, (1950). 226-241.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 209.
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).
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LINKS
| Index entries for sequences related to Hermite polynomials
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FORMULA
| E.g.f.: exp(-x-x^2). a(n) = Sum_{k = 0..floor(n/2)} (-1)^(n-k)*k!*binomial(n, k)*binomial(n-k, k). a(n) = -a(n-1)-2*(n-1)*a(n-2), a(0) = 1, a(1) = -1.
A000186(n) ~ n!^2*exp(1)^(-3)*(a(0) + a(1)/n + a(2)/(2*[n]_2) + ... + a(k)/(k!*[n]_k) + ...), where [n]_k = n*(n-1)*...*(n-k + 1), [n]_0 = 1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 30 2001
a(n)=sum{k=0..n, (-1)^(n-k)*C(k,n-k)*n!/k!}; - Paul Barry (pbarry(AT)wit.ie), Oct 08 2007
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MATHEMATICA
| lst={}; Do[p=HermiteH[n, (1/2)]; AppendTo[lst, p], {n, 0, 2*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 15 2009]
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CROSSREFS
| Cf. A000186.
Sequence in context: A158820 A082437 A039817 * A039922 A192353 A134274
Adjacent sequences: A000318 A000319 A000320 * A000322 A000323 A000324
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KEYWORD
| sign,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Formulae and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 30 2001
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