Search: id:A000436
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%I A000436 M4584 N1955
%S A000436 1,8,352,38528,7869952,2583554048,1243925143552,825787662368768,
%T A000436 722906928498737152,806875574817679474688,1118389087843083461066752,
%U A000436 1884680130335630169428983808,3794717805092151129643367268352
%N A000436 Generalized Euler numbers.
%D A000436 D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 
               689-694; 22 (1968), 699.
%D A000436 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000436 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000436 Michael E. Hoffman, <a href="http://www.emis.ams.org/journals/EJC/Volume_6/
               PDF/v6i1r21.pdf">DERIVATIVE POLYNOMIALS, EULER POLYNOMIALS, AND ASSOCIATED 
               INTEGER SEQUENCES</a> (see Th. 3.3)
%F A000436 E.g.f.: cos x / cos 3x.
%F A000436 For n>0, a(n) = A002114(n)*2^(2n+1) = (1/3)*A002112(n)*2^(2n+1) . - DELEHAM 
               Philippe (kolotoko(AT)wanadoo.fr), Jan 17 2004
%F A000436 a(n)=Sum_{k, 0<=k<=n}(-1)^k*9^(n-k)*A086646(n,k) . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 27 2006
%F A000436 (-1)^n a(n)=1-sum_{i=0,1,...,n-1) (-1)^i*binomial(2n,2i)*3^(2n-2i)*a(i). 
               - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 19 2006
%F A000436 P_{2n}(sqrt(3))/sqrt(3) (where the polynomials P_n() are defined in A155100). 
               [njas, Nov 05 2009]
%p A000436 A000436 := proc(nmax) local a,n,an; a := [1] : n := 1 : while nops(a)< 
               nmax do an := 1-sum(binomial(2*n,2*i)*3^(2*n-2*i)*(-1)^i*op(i+1,a),
               i=0..n-1) : a := [op(a),an*(-1)^n] ; n := n+1 ; od ; RETURN(a) ; 
               end: A000436(10) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 19 2006
%Y A000436 Bisections: A156177 and A156178.
%Y A000436 Sequence in context: A046244 A079485 A158363 this_sequence A015507 A167256 
               A038016
%Y A000436 Adjacent sequences: A000433 A000434 A000435 this_sequence A000437 A000438 
               A000439
%K A000436 nonn,new
%O A000436 0,2
%A A000436 N. J. A. Sloane (njas(AT)research.att.com).

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