%I A130278
%S A130278 1,1,1,6,17,100,529,3766,31121,276984,2755553,29665306,364627801,
%T A130278 4639937380,64952094401,973467571350,15750475301921,264870218828656,
%U A130278 4759194994114369,90124395399063730,1812001488739061417
%N A130278 Number of degree-n permutations such that number of cycles of size 2k-1 
               is odd (or zero) for every k.
%F A130278 E.g.f.: 1/sqrt(1-x^2)*Product_{k>0} (1+sinh(x^(2*k-1)/(2*k-1))).
%e A130278 a(4)=17 because only the following 7 permutations do not qualify: (1)(2)(3)(4), 
               (1)(2)(34), (1)(23)(4), (1)(24)(3), (12)(3)(4), (13)(2)(4) and (14)(2)(3).
%p A130278 g:=(product(1+sinh(x^(2*k-1)/(2*k-1)),k=1..30))/sqrt(1-x^2): gser:=series(g,
               x =0,25): seq(factorial(n)*coeff(gser,x,n),n=0..20); - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Aug 24 2007
%Y A130278 Cf. A003483, A006950, A015128, A102759, A130126, A131942, A130219-A130223.
%Y A130278 Sequence in context: A123189 A047156 A154494 this_sequence A024080 A099436 
               A077022
%Y A130278 Adjacent sequences: A130275 A130276 A130277 this_sequence A130279 A130280 
               A130281
%K A130278 easy,nonn
%O A130278 0,4
%A A130278 Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06 2007
%E A130278 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007