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%I #14 Jun 19 2024 09:28:04
%S 0,1,17,1652,474770,301474214,357901156354,712632435944568,
%T 2204970751341231816,10017874331177386762512,
%U 63973486554110386836270096,554598491512901862814742673168,6344773703149123365957506715989568,93563015826037060521986513216617599504
%N a(n) = Sum_{k=1..n} k! * k^(2*n-1) * |Stirling1(n,k)|.
%F E.g.f.: Sum_{k>=1} (-log(1 - k^2*x))^k / k.
%t nmax=13; Range[0,nmax]!CoefficientList[Series[Sum[(-Log[1 - k^2*x])^k / k,{k,nmax}],{x,0,nmax}],x] (* _Stefano Spezia_, Jun 19 2024 *)
%o (PARI) a(n) = sum(k=1, n, k!*k^(2*n-1)*abs(stirling(n, k, 1)));
%Y Cf. A003713, A373855.
%Y Cf. A220179, A242228, A373858.
%Y Cf. A351136, A373861.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 19 2024