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%I #19 Aug 04 2022 07:35:53
%S 1,1,3,19,217,3821,95761,3214975,137501505,7226764921,455941716481,
%T 33983083953611,2954163633223969,296027886705639973,
%U 33823026186790043841,4363561123325076879991,630392564294402819207041
%N a(n) = Sum_{k=0..n} binomial(n,k)*(n-k)^k*k^k.
%H G. C. Greubel, <a href="/A135749/b135749.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = n!*[x^n] Sum_{k=0..n} exp((n-k)*x)^k * x^k/k!.
%t Table[Sum[Binomial[n,k](n-k)^k k^k,{k,n}],{n,0,20}]+1 (* _Harvey P. Dale_, Oct 08 2012 *)
%o (PARI) a(n)=sum(k=0,n,binomial(n,k)*(n-k)^k*k^k)
%o (PARI) a(n)=n!*polcoeff(sum(k=0,n,exp((n-k)*k*x +x*O(x^n))*x^k/k!),n)
%Y Cf. A000248, A086331, A349965.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 27 2007
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