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A059439 A diagonal of A059438.

%I A059439 #20 Aug 26 2015 11:53:09
%S A059439 0,0,1,2,7,32,177,1142,8411,69692,642581,6534978,72754927,880877928,
%T A059439 11530686953,162331760494,2446380427331,39300220067668,
%U A059439 670480457586813,12106985274788506,230691361507912471,4625811718758963136
%N A059439 A diagonal of A059438.
%C A059439 Self-convolution of A003319. - _Vaclav Kotesovec_, Aug 03 2015
%D A059439 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 262 (#14).
%F A059439 G.f.: (1-1/Sum (k! x^k ))^2.
%F A059439 For n>0, a(n) = A259472(n) + 2*A003319(n). - _Vaclav Kotesovec_, Aug 03 2015
%F A059439 a(n) ~ 2*(n-1)! * (1 - 1/n - 1/n^2 + 1/n^3 + 30/n^4 + 404/n^5 + 5379/n^6 + 76021/n^7 + 1155805/n^8 + 18931873/n^9 + 333434490/n^10), for coefficients see A260913. - _Vaclav Kotesovec_, Aug 03 2015
%e A059439 G.f. = x^2 + 2*x^3 + 7*x^4 + 32*x^5 + 177*x^6 + 1142*x^7 + 8411*x^8 + ...
%t A059439 a[0]=0; a[n_]:=a[n] = n!-Sum[k!*a[n-k], {k,1,n-1}]; Table[Sum[a[k]*a[n-k],{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Aug 03 2015 *)
%t A059439 CoefficientList[Assuming[Element[x, Reals], Series[(1 - x*E^(1/x) / ExpIntegralEi[1/x])^2, {x, 0, 20}]], x] (* _Vaclav Kotesovec_, Aug 03 2015 *)
%Y A059439 Cf. A003319, A259472, A260503, A260913.
%K A059439 nonn,easy
%O A059439 0,4
%A A059439 _N. J. A. Sloane_, Feb 01 2001
%E A059439 More terms from _Vladeta Jovovic_, Mar 04 2001
%E A059439 Prepended a(0)=0, a(1)=0 from _Vaclav Kotesovec_, Aug 03 2015