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A047793 a(n) = Sum_{k=0..n} |Stirling1(n,k)*Stirling2(n,k)|.

%I A047793 #16 Sep 08 2022 08:44:57
%S A047793 1,1,2,12,120,1750,34615,882868,28008694,1076404824,49100939538,
%T A047793 2615329877358,160486317081673,11218516998346216,884855465842682269,
%U A047793 78106000651400369100,7660758993518625156050,829683453926089044978468
%N A047793 a(n) = Sum_{k=0..n} |Stirling1(n,k)*Stirling2(n,k)|.
%H A047793 G. C. Greubel, <a href="/A047793/b047793.txt">Table of n, a(n) for n = 0..290</a>
%p A047793 seq(add((-1)^(n-k)*stirling1(n, k)*stirling2(n, k), k = 0..n), n = 0.. 20); # _G. C. Greubel_, Aug 07 2019
%t A047793 Table[Sum[Abs[StirlingS1[n,k]StirlingS2[n,k]],{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Jul 18 2017 *)
%o A047793 (Maxima) makelist(sum(abs(stirling1(n,k))*stirling2(n,k),k,0,n),n,0,12); /* _Emanuele Munarini_, Jul 01 2011 */
%o A047793 (PARI) {a(n) = sum(k=0,n, (-1)^(n-k)*stirling(n,k,1)*stirling(n,k,2))};
%o A047793 vector(20, n, n--; a(n)) \\ _G. C. Greubel_, Aug 07 2019
%o A047793 (Magma) [(&+[(-1)^(n-k)*StirlingFirst(n,k)*StirlingSecond(n,k): k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Aug 07 2019
%o A047793 (Sage) [sum(stirling_number1(n,k)*stirling_number2(n,k) for k in (0..n)) for n in (0..20)] # _G. C. Greubel_, Aug 07 2019
%o A047793 (GAP) List([0..20], n-> Sum([0..n], k-> Stirling1(n,k)*Stirling2(n,k) )); # _G. C. Greubel_, Aug 07 2019
%Y A047793 Cf. A008275, A008277, A047792, A047794, A047795.
%K A047793 nonn
%O A047793 0,3
%A A047793 _N. J. A. Sloane_