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%I #9 Jun 19 2024 09:28:00
%S 1,1,17,923,107724,22369324,7385651720,3597082257152,2449105468081600,
%T 2238708422118782376,2661994302285967390224,4014423110086784061347592,
%U 7519716937006429200213786240,17194081369411703462470895338272
%N a(n) = Sum_{k=0..n} k^(2*n) * |Stirling1(n,k)|.
%F E.g.f.: Sum_{k>=0} (-log(1 - k^2*x))^k / k!.
%t Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; nmax=13; Range[0,nmax]!CoefficientList[Series[Sum[(-Log[1 - k^2*x])^k / k!,{k,0,nmax}],{x,0,nmax}],x] (* _Stefano Spezia_, Jun 19 2024 *)
%o (PARI) a(n) = sum(k=0, n, k^(2*n)*abs(stirling(n, k, 1)));
%Y Cf. A229261, A351183, A373856.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 19 2024
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