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A122486 a(n) = Sum_{k=0..n} |Stirling1(n,k)|*Bell(k)^2.

%I A122486 #17 May 05 2019 00:32:51
%S A122486 1,1,5,39,425,6053,107735,2321469,59152987,1750362419,59286010621,
%T A122486 2271617296347,97502863649141,4649359584613201,244550369307356039,
%U A122486 14101227268075911837,886551391533830227267,60482082002935189216499
%N A122486 a(n) = Sum_{k=0..n} |Stirling1(n,k)|*Bell(k)^2.
%C A122486 Row sums of the absolute values of the triangle of Stirling1(n,k)*Bell(k)^2:
%C A122486   1;
%C A122486   0,    1;
%C A122486   0,   -1,     4;
%C A122486   0,    2,   -12,    25;
%C A122486   0,   -6,    44,  -150,     225;
%C A122486   0,   24,  -200,   875,   -2250,   2704;
%C A122486   0, -120,  1096, -5625,   19125, -40560,   41209;
%C A122486   0,  720, -7056, 40600, -165375, 473200, -865389, 769129;
%C A122486   ... - _R. J. Mathar_, Jan 27 2017
%F A122486 a(n) = exp(-2)*Sum_{r,s>=0} [r*s]^n/(r!*s!), where [m]^n = m*(m+1)*...*(m+n-1) is the rising factorial.
%F A122486 E.g.f.: Sum_{n>=0} exp( 1/(1-x)^n - 2 ) / n!. - _Paul D. Hanna_, Jul 25 2018
%p A122486 with(combinat): seq(sum(abs(stirling1(n,k))*bell(k)^2,k=0..n),n=0..19); # _Emeric Deutsch_, Oct 08 2006
%Y A122486 Cf. A000110, A059849.
%K A122486 nonn,easy
%O A122486 0,3
%A A122486 _Vladeta Jovovic_, Sep 15 2006, Sep 19 2006
%E A122486 More terms from _Emeric Deutsch_, Oct 08 2006