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%I #12 Feb 06 2025 09:41:38
%S 1,1,10,141,2776,70045,2157156,78452521,3290644288,156380715801,
%T 8304267312100,487328231729581,31318669850761008,2187567259278425557,
%U 165011952533314548676,13368463736048341225425,1157693100510102752463616,106719312722496774534400177,10433609651067618426072766020
%N Main diagonal of the array A380841.
%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(k+n-1,k)/(n-k)!. - _Seiichi Manyama_, Feb 06 2025
%t A380841[n_,k_]:=n!SeriesCoefficient[1/(1-x*Exp[x])^k,{x,0,n}]; Table[A380841[n,n],{n,0,18}]
%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(k+n-1, k)/(n-k)!); \\ _Seiichi Manyama_, Feb 06 2025
%Y Cf. A213643, A380841.
%K nonn,new
%O 0,3
%A _Stefano Spezia_, Feb 05 2025