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 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; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = A126804(n)/2. - Zerinvary Lajos, 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. 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]. H. E. Salzer, Coefficients for expressing the first thirty powers in terms of the Hermite polynomials, Math. Comp., 3 (1948), 167-169. 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, 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, 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, May 03 2007 seq(1/2*mul((n+k), k=1..n), n=0..16); # Zerinvary Lajos, 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, 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: A241710 A318245 A051609 * A327079 A013924 A145560 Adjacent sequences:  A001811 A001812 A001813 * A001815 A001816 A001817 KEYWORD nonn AUTHOR EXTENSIONS More terms and new description from Christian G. Bower, Dec 18 2001 STATUS approved

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Last modified May 26 09:37 EDT 2020. Contains 334620 sequences. (Running on oeis4.)