%I A130714
%S A130714 1,2,3,5,6,10,11,16,19,26,27,41,42,55,64,81,83,114,116,151,168,202,210,
%T A130714 277,289,348,382,460,478,604,623,747,812,942,1006,1223,1269,1479,1605,
%U A130714 1870,1959,2329,2434,2818,3056,3458,3653,4280,4493,5130,5507,6231,6580
%N A130714 Number of partitions of n such that every part divides the largest part 
               and such that the smallest part divides every part.
%F A130714 G.f.: Sum_{i>=0} Sum_(j>0} x^(j+i*j)/Product_{k|i} (1-x^(j*k)).
%p A130714 A130714 := proc(n) local gf,den,i,k,j ; gf := 0 ; for i from 0 to n do 
               for j from 1 to n/(1+i) do den := 1 ; for k in numtheory[divisors](i) 
               do den := den*(1-x^(j*k)) ; od ; gf := taylor(gf+x^(j+i*j)/den,x=0,
               n+1) ; od ; od: coeftayl(gf,x=0,n) ; end: seq(A130714(n),n=1..60) 
               ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2007
%Y A130714 Sequence in context: A018396 A003238 A051839 this_sequence A130689 A024560 
               A000039
%Y A130714 Adjacent sequences: A130711 A130712 A130713 this_sequence A130715 A130716 
               A130717
%K A130714 easy,nonn
%O A130714 1,2
%A A130714 Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 02 2007
%E A130714 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2007