login
Second-order Euler numbers.
(Formerly M1686 N0665)
0

%I M1686 N0665 #20 Apr 18 2014 05:56:04

%S 0,2,6,28,180,662,7266,24568,408360,1326122,30974526,98329108,

%T 3065784540,9596075582,384653685786,1192744081648,59724464976720,

%U 183983154281042,11249503075325046,34489251602450188

%N Second-order Euler numbers.

%D A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 75.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H M. A. Stern, <a href="http://dx.doi.org/10.1515/crll.1880.89.257">Zur Theorie der Eulerschen Zahlen</a>, J. Reine Angew. Math., 79 (1875), 67-98.

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%p F := 2/(exp(x)+exp(-x)): z := ((exp(x)-exp(-x))/(exp(x)+exp(-x)))^2: w := simplify(diff(z,x)): p := proc(n) if n mod 2 = 0 then simplify(subs(x=0,(-1)^(1+floor(n/2))*simplify(diff(diff(F,x$n)/F,x)/w))) else simplify(subs(x=0,(-1)^(1+floor(n/2))*simplify(diff(diff(F,x$n)/simplify(diff(F,x)),x)/w))) fi end: seq(p(n),n=1..28); # _Emeric Deutsch_, Mar 09 2004

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Emeric Deutsch_, Mar 09 2004