%I A001824 M4749 N2031
%S A001824 1,10,259,12916,1057221,128816766,21878089479,4940831601000,
%T A001824 1432009163039625,518142759828635250,228929627246078500875,
%U A001824 121292816354463333793500,75908014254880833434338125
%N A001824 Central factorial numbers.
%D A001824 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001824 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001824 T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 
               2nd. ed. 1949, p. 223, Problem 2.
%D A001824 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
%H A001824 T. D. Noe, <a href="b001824.txt">Table of n, a(n) for n=0..50</a>
%H A001824 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%F A001824 E.g.f.: (arcsin x)^3; that is, a_k is the coefficient of x^(2*k+3) in 
               (arcsin x)^3 multiplied by (2*k+3)! and divided by 6 - Joe Keane 
               (jgk(AT)jgk.org)
%F A001824 a(n) = ((2*n+1)!!)^2 * sum[ k=0..n ] (2*k+1)^(-2).
%F A001824 a(n) ~ pi^2*n^2*2^(2*n)*e^(-2*n)*n^(2*n) - Joe Keane (jgk(AT)jgk.org), 
               Jun 06 2002
%F A001824 (-1)^(n-1)*a(n-1) is the coefficient of x^2 in prod(k=1, 2*n, x+2*k-2*n-1). 
               - Benoit Cloitre and Michael Somos, Nov 22, 2002.
%e A001824 (arcsin x)^3 = x^3 + 1/2*x^5 + 37/120*x^7 + 3229/15120*x^9 + ...
%Y A001824 Cf. A002455, A001825, A049033.
%Y A001824 Right-hand column 2 in triangle A008956.
%Y A001824 Sequence in context: A126468 A024293 A120268 this_sequence A024294 A084999 
               A054593
%Y A001824 Adjacent sequences: A001821 A001822 A001823 this_sequence A001825 A001826 
               A001827
%K A001824 nonn,easy,nice
%O A001824 0,2
%A A001824 N. J. A. Sloane (njas(AT)research.att.com).
%E A001824 More terms from Joe Keane (jgk(AT)jgk.org)