%I A130263
%S A130263 1,1,1,6,14,85,529,3451,26816,243909,2507333,26196841,323194816,
%T A130263 4086482335,57669014597,864137455455,13792308331616,231648908415001,
%U A130263 4211676768746569,79205041816808905,1584565388341689032
%N A130263 Number of degree-n permutations such that number of cycles of size k 
               is odd (or zero) for every k.
%F A130263 E.g.f.: Product_{k>0} (1+sinh(x^k/k)).
%e A130263 a(2)=1 because we have (12) ((1)(2) does not qualify). a(4)=14 because 
               the following 10 permutations of 4 do not qualify: (1)(2)(3)(4), 
               (14)(2)(3), (1)(24)(3), (1)(2)(34), (13)(2)(4), (13)(24), (1)(23)(4), 
               (14)(23), (12)(3)(4) and (12)(34).
%p A130263 g:=product(1+sinh(x^k/k),k=1..40): gser:=series(g,x=0,25): seq(factorial(n)*coeff(gser,
               x,n),n=0..21); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 
               2007
%Y A130263 Cf. A055922, A130219, A130220.
%Y A130263 Sequence in context: A059954 A139257 A056842 this_sequence A077401 A158965 
               A013314
%Y A130263 Adjacent sequences: A130260 A130261 A130262 this_sequence A130264 A130265 
               A130266
%K A130263 easy,nonn
%O A130263 0,4
%A A130263 Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06 2007
%E A130263 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007